Question

Prove the polynomial identity.

(4x2−2)2−(4x2)2=4(1−2x)(1+2x)

Drag and drop the lines of the proof in the correct order to complete the proof.

Answer 1

Proven

Explanation:

We prove the polynomial with factorization. We must first simplify the expression before we can factorize:

`(4\cdot{x^2}-2)\cdot{(4\cdot{x^2}-2)}-16\cdot{x^4}`

`16\cdot{x^4}-8\cdot{x^2}-8\cdot{x^2}+4-16\cdot{x^4}`

`4-16\cdot{x^2}`

4 is the common number and we can take it out of the expression:

`4\cdot{(1-4\cdot{x^2})}`

We can factorize further with the x term being zero. For this to be true we must have -2x and 2x to cancel out and therefore the expression is proven:

`4\cdot{(1-2\cdot{x})}\cdot{(1+2\cdot{x})}`