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Factor expression completely. If an expression is prime, so indicate.$x^{3}+a^{6} y^{3}$

$\left(x+a^{2} y\right)\left(x^{2}+a^{4} y^{2}-a^{2} x y\right)$

Algebra

Chapter 5

Exponents, Polynomials, and Polynomial Functions

Section 8

Summary of Factoring Techniques

Exponents and Polynomials

Polynomials

Missouri State University

McMaster University

Lectures

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Factor each expression com…

01:06

Factor. If an expression i…

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Factor expression complete…

01:29

Factor the given expressio…

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Factor completely, or stat…

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00:27

Factor completely. If a po…

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Factor completely.$x^{…

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02:45

okay, We're gonna go ahead and factor the expression given to us, which is X to the third, plus a to the sixth. Why, to the third First thing we always look for is if there's anything in common between the two terms and there is not in this situation and so that now we realize that we have a two term polynomial, and when we have a two term polynomial, we immediately should think about either the difference of squares or the summer difference of cubes. And I already have the formless list of the top here so we can reference them and it is a some. And so, um, we want Look, what are some of Cuba's forming over here? And these are cubes X to the third. That's a perfect cube. Ageless six. Because it's a multiple of three is a cube, and why did the third is a cube? So we're gonna use the blue formula up here for the sum of cubes and toe. Keep things consistent with my formula. Appear a in this case is going to be equal to X and B is gonna be equal toe a squared. Why? And so we will just use this formal up here. And so it's a plus. Bees that's X plus a squared. Why and then a squared is X squared minus a B so minus a squared X y and then plus B squared plus a to the fourth. Why skirt? So we have X plus a squared wide, and then we have X squared minus a squared X Y plus ayla fourth y squared.

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