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
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
Ex 2 5 6 Write The Following Cubes In Expanded Form Ex 2 5
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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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Write Each Of The Expanded Form 3x 2y 3
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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