Recognize Expression: Recognize the expression to be expanded. We need to expand (5w - 2)^3, which means we will multiply (5w - 2) by itself three times.Begin Expansion: Begin the expansion using the binomial theorem or by multiplying two factors first. Let's multiply (5w - 2) by (5w - 2) to get the first part of our expansion. (5w - 2)(5w - 2) = (5w)^2 - 2(5w)(2) + (2)^2 = 25w^2 - 20w + 4Multiply First Part: Multiply the result from Step 2 by the remaining (5w - 2) factor. Now we take our result, 25w^2 - 20w + 4, and multiply it by (5w - 2). (25w^2 - 20w + 4)(5w - 2)Multiply Remaining Factor: Distribute each term of (25w^2 - 20w + 4) by (5w - 2). We will use the distributive property to multiply each term of the first binomial by each term of the second binomial. 25w^2(5w) + 25w^2(-2) - 20w(5w) - 20w(-2) + 4(5w) + 4(-2) = 125w^3 - 50w^2 - 100w^2 + 40w + 20w - 8Distribute and Multiply: Combine like terms. Now we combine the terms that have the same variable to the same power. 125w^3 - (50w^2 + 100w^2) + (40w + 20w) - 8 = 125w^3 - 150w^2 + 60w - 8

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

(5w-2)^3

Recognize Expression: Recognize the expression to be expanded. $\newline$ We need to expand $(5w - 2)^3$ , which means we will multiply $(5w - 2)$ by itself three times.
Begin Expansion: Begin the expansion using the binomial theorem or by multiplying two factors first. $\newline$ Let's multiply $(5w - 2)$ by $(5w - 2)$ to get the first part of our expansion. $\newline$ $(5w - 2)(5w - 2) = (5w)^2 - 2(5w)(2) + (2)^2$ $\newline$ $= 25w^2 - 20w + 4$
Multiply First Part: Multiply the result from Step $2$ by the remaining $(5w - 2)$ factor. $\newline$ Now we take our result, $25w^2 - 20w + 4$ , and multiply it by $(5w - 2)$ . $\newline$ $(25w^2 - 20w + 4)(5w - 2)$
Multiply Remaining Factor: Distribute each term of $(25w^2 - 20w + 4)$ by $(5w - 2)$ . We will use the distributive property to multiply each term of the first binomial by each term of the second binomial. $25w^2(5w) + 25w^2(-2) - 20w(5w) - 20w(-2) + 4(5w) + 4(-2) = 125w^3 - 50w^2 - 100w^2 + 40w + 20w - 8$
Distribute and Multiply: Combine like terms. $\newline$ Now we combine the terms that have the same variable to the same power. $\newline$ $125w^3 - (50w^2 + 100w^2) + (40w + 20w) - 8$ $\newline$ = $125w^3 - 150w^2 + 60w - 8$