Question

Factorize: ^ 4 − ^4​

Answer 1

Step-by-step explanation:

Let x

2

=p, then the equation 4x

4

+7x

2

−2 becomes 4p

2

+7p−2

Consider the expression 4p

2

+7p−2 and factorise it as follows:

4p

2

+7p−2=4p

2

+8p−p−2=4p(p+2)−1(p+2)=(4p−1)(p+2)

Now, substitute the value of p as p=x

2

:

(4p−1)(p+2)=(4x

2

−1)(x

2

+2)=(2x+1)(2x−1)(x

2

+2) (Using identity a

2

−b

2

=(a+b)(a−b))

Hence, 4x

4

+7x

2

−2=(2x+1)(2x−1)(x

2

+2)