Question

factorise the following
2x⁴-32​

Answer 1

Step-by-step explanation:

Given : 2x

4

−32

By taking 2 as common

2x

4

−32=2(x

2

−16)

We can further write it as

2x

4

−32=2[(x

2

)

2

−4

2

]

Based on equation a

2

−b

2

=(a+b)(a−b)

We get,

2x

4

−32=2[(x

2

+4)(x

2

−4)]

So we get,

2x

4

−32=2[(x

2

−2

2

)(x

2

+4)]

By using the formula

2x

4

−32=2[(x+2)(x−2)(x

2

+4)]

2x

4

−32=2(x+2)(x−2)(x

2

+4)

Answer 2

Answer:

2x^4-32

= 2(x^4-16) {taking 2 common}

= 2{(x^2)^2-4^2} { taking the square of x^2 & 4instead of x^4 & 16}

= 2(x2+4) (x^2-4) {using the formula a^2-b^2 = (a+b) (a-b)}

= 2(x^2+4) (x^2-2^2). { taking 2^2 instead of 4}

= 2(x^2+4) ( x+2)(x-2). {using the same formula of a^2-b^2}

The required answer is 2(x^2+4) (x+2)(x-2)

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