Factor completely: (x+6)^(3)-(x+6)^(4) Answer:

Recognize Common Base: Recognize the common base in both terms. Both terms have the common base of (x+6). We can factor this base out using the difference of powers factoring rule.Apply Factoring Rule: Apply the difference of powers factoring rule. The difference of powers factoring rule states that a^n - b^n = (a - b)(a^(n-1) + a^(n-2)b + ... + ab^(n-2) + b^(n-1)) when n is a positive integer. In this case, we can consider a = (x+6) and n = 4 to apply the rule.Factor Out Common Base: Factor out the common base (x+6)^(3). We can write the expression as (x+6)^(3) * (1 - (x+6)).Simplify Expression: Simplify the factored expression. Now we simplify the expression inside the parentheses: 1 - (x+6) = 1 - x - 6 = -x - 5.Write Final Form: Write the final factored form. The completely factored form of the expression is (x+6)^(3) * (-x - 5).

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Factor completely:

(x+6)^(3)-(x+6)^(4)
Answer:

Factor completely: $\newline$ $(x+6)^{3}-(x+6)^{4}$ $\newline$ Answer:

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Math Problems

Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(x+6)^{3}-(x+6)^{4}

\newline

Answer:

Recognize Common Base: Recognize the common base in both terms. $\newline$ Both terms have the common base of $(x+6)$ . We can factor this base out using the difference of powers factoring rule.
Apply Factoring Rule: Apply the difference of powers factoring rule. $\newline$ The difference of powers factoring rule states that $a^n - b^n = (a - b)(a^{n-1} + a^{n-2}b + \ldots + ab^{n-2} + b^{n-1})$ when $n$ is a positive integer. In this case, we can consider $a = (x+6)$ and $n = 4$ to apply the rule.
Factor Out Common Base: Factor out the common base $(x+6)^{3}$ . We can write the expression as $(x+6)^{3} \times (1 - (x+6))$ .
Simplify Expression: Simplify the factored expression. $\newline$ Now we simplify the expression inside the parentheses: $1 - (x+6) = 1 - x - 6 = -x - 5$ .
Write Final Form: Write the final factored form. $\newline$ The completely factored form of the expression is $(x+6)^{3} \cdot (-x - 5)$ .