Question

Factor 4x^4yz-16y^3z

Answer 1

4x⁴yz - 16y³z = 4yz(x² - 2y)(x² + 2y)

Explanation:

`4x^4yz-16y^3z\\\\4x^4yz=4yz\cdot x^4\\\\16y^3z=4yz\cdot4y^2\\\\4x^4yz-16y^3z=4yz\cdot x^4-4yz\cdot4y^2=4yz(x^4-4y^2)\\\\x^4-4y^2=x^(2\cdot2)-2^2y^2=(x^2)^2-(2y)^2=(x^2-2y)(x^2+2y)\\\\Used:\\\\(a^n)^m=a^(nm)\\\\(ab)^n=a^nb^n\\\\a^2-b^2=(a-b)(a+b)\\\\4x^4yz-16y^3z=4yz(x^2-2y)(x^2+2y)`