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 , Ex 25, 4 Expand each of the following, using suitable identities (x 2y 4z)2 (x 2y 4z)2 Using (a b c)2 = a2 b2 c2 2ab 2bc 2ac Where a = x , bExpand the following ` (i) (3a2b)^ (3) (ii) ( (1)/ (x) (y)/ (3))^ (3)` (iii) ` (4 (1)/ (3x))^ (2)` Watch later Share Copy link Info Shopping Tap to unmute If playback doesn't begin
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Expand (1/x+y/3)^3 class 9- 8 madhu hey mates here ur answer = (1/ x)^3 (y/3)^3 3 (1/x) (1/y) (1/xy/3) = 1/x^3 y^3 /27 y/x^2 y/3x dome7w and 12 more users found this answer helpful heart outlined Thanks 8 starTo solve a pair of equations using substitution, first solve one of the equations for one of the variables Then substitute the result for that variable in the other equation x2y=3,3xky=1 x − 2y = 3,3x ky = 1 Choose one of the equations and solve it
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Answer 6 x y 2 x z Apply Multiplicative Distribution Law 2 x * 3 y 2 x zRemove the parentheses 2 x * 3 yClick here👆to get an answer to your question ️ Expand the following polynomial (x y √(3))^2 (x^2y xy^2 )^2 (x y )^2Expand 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!
The Binomial Theorem is the method of expanding an expression which has been raised to any finite power A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc Binomial Expression A binomial expression is an algebraic expression which contains two dissimilar terms Ex a b, a 3 b 3, etc 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 3(2x)(1) (2x 1) = 8x3 1 6x(2x 1) = 8x3 1 12x2 6x = 8x3 12x2 6x 1 Ex 25, 6 Write the following cubes in expanded form (ii) (2a 3b)3 (2a 3b)3 Using (x y)3 = x3 y3 3xy(x y) Where x = 2a & y = 3b = (2a)3 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 terms in the other brackets, but never multiply two or more terms in the same bracket
Explain your reasoning a^5 * b^3, b^8, a^4 * b^4, a^8, and a * b^7 because all of the degrees of the terms are 8How To Given a binomial, write it in expanded form Determine the value of n \displaystyle n n according to the exponent Evaluate the k = 0 \displaystyle k=0 k = 0 through k = n \displaystyle k=n k = n using the Binomial Theorem formulaExpand each of the following a) (x2)(x3) b) (ab)(c3) c) (y − 3)(y 2) d) (2x1)(3x−2) e) (3x− 1)(3x1) f) (5x− 1)(x− 5) g) (2p3q)(5p−2q) h) (x2)(2x2 − x− 1) Answers 1 a) 5x b) 2y −6 c) 12−4a d) 2xx2 e) pq 3p f) −6−3a g) st−s2 h) −2b6 i) 10ab15ac j) −2xy 5y2 2
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Factor x^3y^3 x3 − y3 x 3 y 3 Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 abb2) a 3 b 3 = ( a b) ( a 2 a b b 2) where a = x a = x and b = y b = y (x−y)(x2 xyy2) ( x y) ( x 2 x y y 2)10 If x – 1/x = 3 2√2, find the value of ¼ (x 3 – 1/x 3) Solution It is given that, x – 1/x = 3 2√2 So, x 3 – 1/x 3 = (x – 1/x) 3 3(x – 1/x) = (3 2√2) 3 3(3 2√2) By using the formula, (ab) 3 = a 3 b 3 3ab (a b) = (3) 3 (2√2) 3 3 (3) (2√2) (3 2√2) 3(3 2√2) = 27 16√2 54√2 72 9 6√2 = 108 76√2 Hence,Steps for Solving Linear Equation x 3 ( y 1 ) = 2 x 8 x 3 ( y 1) = 2 x 8 Use the distributive property to multiply 3 by y1 Use the distributive property to multiply 3 by y 1 x3y3=2x8 x 3 y 3 = 2 x 8 Subtract x from both sides Subtract x from both sides
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(4x^{3}yxy^{3}4x)(7x4xy^32x^{2}) Which of the following is equivalent to the expression above?Short Solution Steps \frac { { x }^ { 2 } { y }^ { 2 } } { { x }^ { 3 } { y }^ { 3 } } x 3 − y 3 x 2 − y 2 Factor the expressions that are not already factored Factor the expressions that are not already factored \frac {\left (xy\right)\left (xy\right)} {\left (xy\right)\left (x^ {2}xyy^ {2}\right)}Bexpand the United States from the Atlantic to the Pacific Ocean Cwarn European countries not to form new colonies in South America Dlimit the Math Expand and simplify (p3)(p7) Civics Which of the following would contribute most to the creation of a strong economy?
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Expand each of the following (i)`(x/2y/3)^2` (ii) `(x5)(x3)` More Related Question & Answers Expand the following by binomial theorem (x^23/x)^5, x!=0Expand the following using binomial theorem (x 3 − 1) 3 1 x 5x 3 − 1) 3 1 x 5 AnswerGet answer Using binomial theorem, expand each of the following(x1,y)^(5)
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So in this particular case we get (x y)6 = 6C0x6 6C1x6−1y1 6C2x6−2y2 6C3x6−3y3 6C4x6−4y4 6C5x6−5y5 6C6y6 = x6 6x5y 15x4y2 x3y3Mathematics, 1850, Kkampudiaa Expand the following 2 (x3) Expand the following expression 5x(3 – 7y) alexia170 alexia170 Mathematics College answered Expand the following expression 5x(3 – 7y) 1 See answer alexia170 is waiting for your help Add your answer and earn points
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Expand the following 1 (x 6y)3 = 2 (ab – 2mn)3 = 3 (3xy – 5)3 = 4 (4x2y – y)3 = 5 (3a2b2 b)3 = MafiaQueen07 is waiting for your help Add your answer and earn points New questions in Math The Lilliputians are 6 inches tall Gulliver is 6 feet tall What is the ratio of his height to the average height of the people in LilliputExpand the following Knockout JEE Main April 21 (One Month) Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support, 9(5x 1) ÷ 3y From the expression above, provide an example of each of the following sum, term, product, factor, quotient, and coefficient If any a re not present, write "not present" i need in 1 hour
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(4x^{3}yxy^{3}4x)(7x4xy^32x^{2}) Which of the following is equivalent to the expression above?⋅(1)3−k ⋅(−x)k ∑ k = 0 3 3!Mathematics, 0631 zanestone12 Use the distributive property to expand the following expression 2(21x 3y 18)
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The Binomial Theorem gives a time efficient way to expand binomials raised to a power and may be stated as (x y)n = n ∑ r=0nCrxn−ryr, where the combination nCr = n!Expand\3(x6) expand\2x(xa) expand\(2x4)(x5) expand\(2x5)(3x6) expand\(4x^23)(3x1) expand\(x^23y)^3( 3 k)!
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and morePascal's Triangle is probably the easiest way to expand binomials It's much simpler to use than the Binomial Theorem, which provides a formula for expanding binomials The formula for Pascal's Triangle comes from a relationship that you yourself might be able to see in the coefficients below (x y) 0 (x y) 1 (x y)² (x y) 3 (x y) 4Suppose we want to expand (2xy)3 We pick the coefficients in the expansion from the relevant row of Pascal's triangle (1,3,3,1) As we move through the terms in the expansion from left to right we remember to decrease the power of 2x and increase the power of y So, (2xy)3 = 1(2x)3 3(2x)2y 3(2x)1y2 1y3 = 8x3 12x 2y 6xy y3 Example
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TASK 2 Expand the following using the binomial theorem and Pascal's triangle 5 In the expansion of (3a 4b)^8, which of the following are possible variable terms? Expand the following `(i) (3a2b)^(3) (ii) ((1)/(x)(y)/(3))^(3)` (iii) `(4(1)/(3x))^(2)`👍 Correct answer to the question (1/x y/3)³ Expand The Following pls help eanswersin
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Get answer Expand the following (i) (3a2b)^(3) (ii) ((1),(x)(y),(3))^(3) (iii) (4(1),(3x))^(2) Apne doubts clear karein ab Whatsapp par bhi Try it nowClick here👆to get an answer to your question ️ If x y = 12 and xy = 27 , find the value of x^3 y^3Expand the following binomial expression using the binomial theorem ( x y) 4 The expansion will have five terms, there is always a symmetry in the coefficients in front of the terms We use the binomial theorem to expand our binomial ( x y) 4 = 1 x 4 y 0 4 1 (
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