Question

Factorise: ^4 + ^4 + ^2^2​

Answer 1

Answer:

4x4+7x2−2=(2x+1)(2x−1)(x2+2)

Step-by-step explanation:

Let x2=p, then the equation 4x4+7x2−2 becomes 4p2+7p−2

Consider the expression 4p2+7p−2 and factorise it as follows:

4p2+7p−2=4p2+8p−p−2=4p(p+2)−1(p+2)=(4p−1)(p+2)

Now, substitute the value of p as p=x2:

(4p−1)(p+2)=(4x2−1)(x2+2)=(2x+1)(2x−1)(x2+2)        (Using identity a2−b2=(a+b)(a−b))

Hence, 4x4+7x2−2=(2x+1)(2x−1)(x2+2)

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