Expand (xy)^3 (x y)3 ( x y) 3 Use the Binomial Theorem x3 3x2y3xy2 y3 x 3 3 x 2 y 3 x y 2 y 3Expand the followinga) 3(x 5)b) 4(x 4)c) 2(5x 1)d) 7(x 9y)In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomialAccording to the theorem, it is possible to expand the polynomial (x y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b c = n, and the coefficient a of each term is a specific positive
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Expand the following (1/x y/3)^3- Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries Students (upto class 102) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (MainsAdvance) and NEET can ask questions from any subject and get quick answers by⋅(1)3−k ⋅(−x)k ∑ k = 0 3
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The calculator allows you to expand and collapse an expression online , to achieve this, the calculator combines the functions collapse and expand For example it is possible to expand and reduce the expression following ( 3 x 1) ( 2 x 4), The calculator will returns the expression in two forms expanded and reduced expression 4 14 ⋅ xThere's no easy, or more or less generally useful, expansion of this thing You could try though $$\log(xy)=\log\left(x\left(1\frac{y}{x}\right)\right)=\log x\log\left(1\frac{y}{x}\right)$$ The above is assuming $\,x>0\,$, and it doesn't look that nice or useful, does it?The quadratic equation who roots are 2√5 and 2√5
= x2 − 17x70 Example Expand (x6)(x− 6) (x6)(x−6) = x 2− 6x6x− 36 = x 2− 36 Example Expand (2x−3)(x1) (2 x−3)( 1) = 2 2 2 3 = 2x2 −x 3 Expand (3x−2)(3x2) (3x− 2)(3x2) = 9x 6x−6x−4 = 9x − 4 Exercises 2 Expand each of the following a) (x2)(x3) b) (ab)(c3) c)To generate Pascal's Triangle, we start by writing a 1 In the row below, row 2, we write two 1's In the 3 rd row, flank the ends of the rows with 1's, and add latex11/latex to find the middle number, 2 In the latexn\text{th}/latex row, flank the ends of the row with 1'sBut who knows, perhaps under certain circumstances
Transcript Ex 25, 6 Write the following cubes in expanded form (i) (2x 1)3 (2x 1)3 Using (a b)3 = a3 b3 3ab(a b) Where a = 2x & b =1 = (2x)3 (1)3 3Samacheer Kalvi 12th Books Solutions Menu Toggle Tamil Nadu 12th Model Question Papers;Question 85 (viii) Expand the following, using suitable identities (4x 5 y 4)(4x 5 3y 4) Mathematics NCERT Exemplar Standard VIII Q 5 Question 85 (ix) Expand the following, using suitable identities (2x 3 − 2 3)(2x 3 2a 3) Mathematics NCERT Exemplar Standard VIII
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And (Σι αι)2 Construct an example to show that, in general, theseExpand lo g y 2 x 3 find the number of digits in (1) 3 4 3, (2) 3 2 7, and (3) 3 6 2, and the position of the first significant figure in (4) 3 − 1 3, (5) 3 If a = 3 b = 0 c = 2 and d = 1 find the value of 3a 2b – 6c 4d asked in Class VI Maths by priya12 Expert (748k points) substitution (including use of brackets as grouping symbols) 0 votes 1 answer
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Expand the following `(i) (3a2b)^(3) (ii) ((1)/(x)(y)/(3))^(3)` (iii) `(4(1)/(3x))^(2)`Expand the following 3(x4) 4(2m3) answers 1) 3x 12 2) 8m 12 to expand the following, all you have to do is to distribute the number outside the parentheses to each terms within the parentheses expand and simplify 3(x4)2(x5) 4(d1)5(d6) 4(w5)3(w1) answersExample 49 Find the expansions of the following, up to the term in x3 In each case, state the range of aliditvy for x (1−x)1/3, (12x)−2 Example 410 Find the expansion of √ 1x up to the term in x2 By taking x = 1/4, use your expansion to nd an approximation to √ 5, giving your answer as a fraction (1x)1/2 = 1 1 2 x 1 2 (1
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Find an answer to your question Expand And Simplify The Following (x3)(x3)(3x2) (2x1)(x2)(x3) (x3)(2x1)(3x2)Expand 1 2 x 3 We pick the coefficients in the expansion from the row of Pascal's triangle (1,3,3,1) Powers of 2 x increase as we move left to right Any power of 1 is still 1 1 2 x 3 = 1(1)3 3(1)2 2 x 3(1)1 2 x 2 1 2 x 3 = 1 6 x 12 x2 8 x3 Exercises 2 Use Pascal's triangle to expand the following binomial expressions 1 (13xG EXPECTATION RULES AND DEFINITIONS a, b are any given constants X, Y are random variables The following apply NOTE we'll use a few of these now and others will come in handy throughout the semester 1 ( X 2 2X µX 2 µX) = Expand the square E( X 2)
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Expanding the following in ascending powers of x (i) 2 4 (1 x x) (ii) 2 4 (2 x x ) 5 Find (i) the 5 th term in the expansion of 10 2 3 2x x (ii) the 6 th term in the expansion of 15 2 y x 2 (iii) the 8 th term in the expansion of 12 2 x x (iv) the 7 th term in the expansion of 9 4x 5 5 2x 6 3 Let f(x) = 3x2 x 6 ( x 2) ( x2 4) (i) Express f(x) in partial fractions (ii) Hence obtain the expansion of f(x) in ascending powers of x, up to and including the term in x2 4 Express (3 4x)1 2 as a series of descending powers of xSolution The expansion is given by the following formula ( a b) n = ∑ k = 0 n ( n k) a n − k b k, where ( n k) = n!
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Find the product of two binomials Use the distributive property to multiply any two polynomials In the previous section you learned that the product A (2x y) expands to A (2x) A (y) Now consider the product (3x z) (2x y) Since (3x z) is in parentheses, we can treat it as a single factor and expand (3x z) (2x y) in the sameType the following First type the equation 2x3=15 Then type the @ symbol Then type x=6 Try it now 2x3=15 @ x=6 Clickable Demo Try entering 2x3=15 @ x=6 into the text box After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x3=15 2(6)3 = 15 The calculator prints "True" to let you know that the answer Explanation (x −y)3 = (x − y)(x −y)(x −y) Expand the first two brackets (x −y)(x − y) = x2 −xy −xy y2 ⇒ x2 y2 − 2xy Multiply the result by the last two brackets (x2 y2 −2xy)(x − y) = x3 − x2y xy2 − y3 −2x2y 2xy2 ⇒ x3 −y3 − 3x2y 3xy2 Always expand each term in the bracket by all the other
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Samacheer Kalvi 11th Books Solutions Menu Toggle Tamil Nadu 11th Model Question PapersSolution Steps (x1) (x3) ( x 1) ( x 3) Apply the distributive property by multiplying each term of x1 by each term of x3 Apply the distributive property by multiplying each term of x 1 by each term of x 3 x^ {2}3xx3 x 2 3 x x 3 Combine 3x A number line from negative 5 to 5 in increments of 1 An open circle is at 3 and a bold line starts at 3 and is pointing to the right A number line from negative 5 to 5 in increments of 1 An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left A number line from negative 5 to 5 in increments of 1
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To expand this, we're going to use binomial expansion So let's look at Pascal's triangle 1 1 1 1 2 1 1 3 3 1 Looking at the row that starts with 1,3, etc, we can see that this row has the numbers 1, 3, 3, and 1 These numbers will be the coefficients of our expansion So to expand ,Our online expert tutors can answer this problem Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Algebra Expand using the Binomial Theorem (1x)^3 (1 − x)3 ( 1 x) 3 Use the binomial expansion theorem to find each term The binomial theorem states (ab)n = n ∑ k=0nCk⋅(an−kbk) ( a b) n = ∑ k = 0 n n C k ⋅ ( a n k b k) 3 ∑ k=0 3!
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Start your free trial In partnership with You are being redirected to Course Hero I want to submit the same problem to Course Hero CancelMathematics RS Agarwal Standard IX Q 1 Expand each of the following, using suitable identities (i) ( x 2 y 4 z) 2 (ii) ( 2 x − y z) 2 (iii) ( − 2 x 3 y 2 z) 2 (iv) ( 3 a − 7 b − c) 2 (v) ( − 2 x 5 y − 3 z) 2 (vi) 1 4 a − 1 2 b 1 2 For example, if we want to confirm that x=6 is a solution to the equation x 3 − 3 x 2 − 16 x = 12 the following Mathematica command accomplishes this Simplify x^3 3 x^2 16 x == 12, x == 6 Out 15= True The Expand command expands a function or
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1 Expand the following expressions (6 mks) a (x2 y)(2x z2 y) b (8x2 3y 2)(x y) c (y 7)(y3) 2 Determine the corresponding quadratic equation of the form ax² bx c = 0 given the following pairs of roots (6 mks) a x = 7,x = 11 b x = 21, x = 51 c x = 5,X = ?3 Solve the following quadratic equations using the Expand each of the following, using suitable identities (i) (x 2y 4z) 2 1 Using formula, (x – y) 3 = x 3 – y 3 – 3xy(x – y) (99) 3 = (100 – 1) 3 Factorise each of the following (i) 8a 3 b 3 12a 2 b 6ab 2 Solution 8a 3 b 3 12a 2 b 6ab 2 can also be written as (2a) 3 b 3 3
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Students can Download Maths Chapter 3 Algebra Ex 31 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 3 Chapter 3 Algebra Ex 3131 Expand the following (1 − 4) 1 6) (b a − 2 5) 2 (y x 3 3) 2 1 ( x 4 4) 4 3 (y x − 5 Expand 7) 7 2 ( x in descending powers of x up to the term in 5 x 6 Expand 8) 3 2 (− x in ascending powers of x up to the term in 2 x Express the expansion of each of the following with summation notation (7 − 8) 7 5) 6 ( x 8 6) 5Expand (3 x − 4 y 5 z) 2 is equal to 9 x 2 1 6 y 2 2 5 z 2
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Find an answer to your question Expand each of the following, using suitable identities i) (2xy)² ii) (3x 5)² ² iii) (x 1/3 ) ² iv) (4x 5) (4x 5) v)2X,Y, Υ3) 1 Σ, 8X,Y, 2 10 Explain the difference between Σε α?Calculate/expand the following (a) Σ52 , (b) 3 (c) Στ = Π (d) Σ12 = 72 N I (1) Σy = 1=1 9 Show that (a) Σ (X Y;) Σ Χ ΣΥ 2 Σ, Χ, (6) Σ(Χ?
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2x3y=52y2xy=122 multiplied by X plus 3 multiplied by Y equals 5 2 multiplied by Y (Y) squared by 2 plus X multiplied by Y equals 12 A factory has a container filled with 358 litres of cold drink In how many bottles, each of 250 ml capacity, can it be filled?= 1 ⋅ 2 ⋅ ⋅ n We have that a = 2 x, b = 5, and n = 3 Therefore, ( 2 x 5) 3 = ∑ k = 0 3 ( 3 k) ( 2 x) 3 − k 5 k Now, calculate the product for every value of k from 0 to 3 Thus, ( 2Write expression log(x7y7 z7) log ( x 7 y 7 z 7) as a sum or difference of logarithms with no exponents Simplify your answer completely log(x7y7 z7) = log ( x 7 y 7 z 7) = Get help Box 1 Enter your answer as an expression Example 3x^21, x/5, (ab)/c Be sure your variables match those in the question ↑
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