Question

Factories :
${x}^{4} - (x - y) ^{4}$
${a}^{4} - 2a {}^{2} b {}^{2} + b {}^{4}$
​

Answer 1

Answer:

Main Aim:

• To factories x⁴-(x-y)⁴ and a⁴-2a²b²+b⁴.

Let us factories the first one.

a) x⁴-(x-y)⁴ (This is in form of identity (a²-b²))

= (x²)²-[(x-y)²]² (Exponents are in form of Multiplication)

= [x+(x-y)[x-(x-y)]

(As we know, (a-b)² = (a+b)(a-b); Thus, this is the factorised form where x is a and (x-y) is b)

or,

$\tt\blue{\boxed{[x+(x-y)] \ [x-(x-y)]}}$

Let us factories the second one.

b) a⁴-2a²b²+b⁴ (In the form of identity a²-2ab+b²)

= (a²)²+(b²)²-2(a²b²) {Now, divided the exponents}

= (a²-b²)² {Now, inform of (a-b)²}

= (a²-b²) (a²-b²) {Factorised form; As we know (a-b)² = a²-2ab+b², hence, this will be the answer}

or,

$\tt\blue{\boxed{({a}^{2}-{b}^{2}) \ ({a}^{2}-{b}^{2})}}$

Answer 2

Answer:

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