Question

(x+y)4-(x-y)4 factorisation

Answer 1

(x+y)^4 - (x-y) ^4

={(x+y)²}² - {(x-y)²}²

We know that a²-b² =(a+b)(a-b)

So,

{(x+y)² +(x-y)²}{(x+y)²-(x-y)²}

={(x²+2xy+y²)+(x²-2xy+y²)}{(x²+2xy+y²)-(x²-2xy+y²)}

=(x²+2xy+y²+x²-2xy+y²)(x²+2xy+y²-x²+2xy-y²)

=(2x²+2y²)(4xy)

=2(x²+y²)(4xy)

=8xy(x²+y²)

Answer 2

The answer to the factorisation is, 8xy (x²+y²)

Given : The given algebraic expression is, (x+y)⁴-(x-y)⁴

To find : The factorisation of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the given algebraic expression)

Here, we will be using general algebraic formula.

So,

= (x+y)⁴-(x-y)⁴

= {(x+y)²}² - {(x-y)²}²

= {(x+y)²+(x-y)²} {(x+y)²-(x-y)²}

= {(x²+2xy+y²)+(x²-2xy+y²)}{(x²+2xy+y²)-(x²-2xy+y²)}

= (x²+2xy+y²+x²-2xy+y²) (x²+2xy+y²-x²+2xy-y²)

= (2x²+2y²) (4xy)

= 2(x²+y²) (4xy)

= 2 (4xy) (x²+y²)

= 8xy (x²+y²)

(This cannot be further factorised. That's why, this will be considered as the final result.)

Used formula :

• a²-b² = (a+b) (a-b)
• (a+b)² = a²+2ab+b²
• (a-b)² = a²-2ab+b²

Hence, the answer to the factorisation is, 8xy (x²+y²)