Question

derive (x-y)^3
best answer will be brainliest ​

Answer 1

$\sf\blue{(x - y)^3}$

Using identity : $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$

We get,

$\sf\orange{=> (x - y)^3}$

$\sf\orange{=> x^3 - y^3 - 3×x×y(x-y)}$

$\sf\orange{=> x^3 - y^3 - 3x^2y + 3xy^2}$

Answer 2

Answer:

Let's solve this by "algebraic" method.

(x-y)³.

We know that a³=a×a×a

Thus, (x-y)³=(x-y)(x-y)(x-y)

First, simplify the first two terms.

(x-y)(x-y)

=(x)(x)+(x)(−y)+(−y)(x)+(−y)(−y) ............( Using distributive property)

=x²−xy−xy+y² .............(Simplifying)

=x²−2xy+y².

Thus, (x-y)(x-y)=x²−2xy+y².

We need to further multiply the product with (x-y).

(x²−2xy+y²)(x−y)

=(x²)(x)+(x²)(−y)+(−2xy)(x)+(−2xy)(−y)+(y²)(x)+(y²)(−y) ...(distributive property)

=x³−x²y−2x²y+2xy²+xy²−y³............(simplify)

=x³−3x²y+3xy²−y³.

Thus,(x-y)³=x³−3x²y+3xy²−y³.

HOPE THIS HELPS :D