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larisa86 [58]
3 years ago
9

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

Mathematics
1 answer:
Iteru [2.4K]3 years ago
6 0

Answer:

<h2>4x⁴yz - 16y³z = 4yz(x² - 2y)(x² + 2y)</h2>

Step-by-step 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)


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