Question

Prove the polynomial identity.

Answer 1

Answer:

Proven

Step-by-step 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:

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