Question

factories it 16x^4-1​

Answer 1

Answer:

16x^4-1 = (4x^2 + 1) (2x + 1) (2x -1)

remember

(a,^2-b^2) (a+b) (a-b)

(16x^4-1) is of this form ( with a = 4x^2) and b = 1)

so,

(16x^2-1) = (4x^2 + 1) (4x^2-1)

but we know that (4x^2-1) is also of this form ( with a = 2x and b = 1)

so, (4x^2-1) = (2x + 1) ( 2x-1)

and completly factoried we have

(16x^2 -1) = ( 4x^2-1) (2x + 1) ( 2x -1) (ans)

hope it helps you.

Answer 2

Explanation:

Remember

XXX(a2−b2)=(a+b)(a−b)

(16x4−1) is of this form (with a=(4x2)and b=1).

So

XXX(16x4−1)=(4x2+1)(4x2−1)

...but we note that (4x2−1) is also of this form (with a=2x and b=1)

So (4x2−1)=(2x+1)(2x−1)

and, completely factored we have

XXX(16x4−1)=(4x2+1)(2x+1)(2x−1)

Answer

16x4−1=(4x2+1)(2x+1)(2x−1)