Find each product. (a−$$b)(a2+ab+b2)(a-b)(a^2$+ab+b^2)$$

Ch. P - Fundamental Concepts of Algebra

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problema 88

Capitolo 1, Problema 88

Find each product. $(a - b) (a^{2} + a b + b^{2})$

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Recognize that the expression $(a - b)(a^2 + ab + b^2)$ matches the form of the difference of cubes factorization, where $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.

Understand that multiplying $(a - b)$ by $(a^2 + ab + b^2)$ will give you the expanded form of $a^3 - b^3$.

To verify, apply the distributive property (also known as FOIL for binomials) by multiplying each term in the first parenthesis by each term in the second parenthesis:

Calculate $a \times a^2 = a^3$, $a \times ab = a^2b$, $a \times b^2 = ab^2$, $-b \times a^2 = -a^2b$, $-b \times ab = -ab^2$, and $-b \times b^2 = -b^3$.

Combine like terms: notice that $a^2b$ and $-a^2b$ cancel out, as do $ab^2$ and $-ab^2$, leaving you with $a^3 - b^3$.

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