The expansion of x-y3 is x3-y3-3 x2 y-3 x y2A- x3-y3-3 x2 y-3 x y2B- x3-y3-3 x2 y-3 x y2

The correct option is B x3 + y3 3x2y + 3xy2 (x + y)^3 = (x + y)(x + y)^2 = (x + y)(x^2 + 2xy + y^2) (x + y)^3 = x(x^2 + 2xy + y^2) + y(x^2 + 2xy + y^2) = x^3 ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a-b)^3

The expansion...

Question

The expansion of ${(x + y)}^{3}$ is $x^{3} + y^{3} + 3 x^{2} y - 3 x y^{2}$

x³ + y³ + 3x²y - 3xy²

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x³ + y³ - 3x²y + 3xy²

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Solution

The correct option is B
x³ + y³ - 3x²y + 3xy²

${(x + y)}^{3} = (x + y) {(x + y)}^{2}$
$= (x + y) (x^{2} + 2 x y + y^{2})$

${(x + y)}^{3} = x (x^{2} + 2 x y + y^{2}) + y (x^{2} + 2 x y + y^{2})$
$= x^{3} + 2 x^{2} y + x y^{2} + x^{2} y + 2 x y^{2} + y^{3}$

$= x^{3} + y^{3} + 3 x^{2} y + 3 x y^{2}$

So, The given statement is false.

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Similar questions

The expansion of ${(x + y)}^{3}$ is

Q. factorise

x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 8

Q. Factorise:

x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 125 = 0

Question 59 (a)

What should be added to $x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}$ to get $x^{3} + y^{3} ?$

Q. If

x^{3} + y^{3} + 3 x^{2} y + 3 x y^{2} = 27,

then

\frac{d y}{d x} = - 1

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The expansion of (x+y)3 is x3+y3+3x2y−3xy2

The correct option is B x3 + y3 - 3x2y + 3xy2 (x+y)3=(x+y)(x+y)2 =(x+y)(x2+2xy+y2) (x+y)3=x(x2+2xy+y2)+y(x2+2xy+y2) =x3+2x2y+xy2+x2y+2xy2+y3 =x3+y3+3x2y+3xy2 So, The given statement is false.

The expansion of ${(x + y)}^{3}$ is $x^{3} + y^{3} + 3 x^{2} y - 3 x y^{2}$