Factor completely: 9(3x-5)^(6)+(3x-5)^(7) Answer:

Identify Common Factor: Identify the common factor in both terms. The expression given is 9(3x-5)^(6)+(3x-5)^(7). Both terms have a common factor of (3x-5)^(6).Factor Out Common Factor: Factor out the common factor from both terms. We can factor out (3x-5)^(6) from both terms to simplify the expression. Factored Form: (3x-5)^(6) * [9 + (3x-5)]Simplify Inside Brackets: Simplify the expression inside the brackets. Now we simplify the expression inside the brackets by adding the constant term 9 to the term (3x-5). Simplified Form: (3x-5)^(6) * (3x-5 + 9)Combine Like Terms: Combine like terms inside the brackets. Inside the brackets, we combine the like terms 3x and -5 + 9. Combined Form: (3x-5)^(6) * (3x + 4)Write Final Form: Write the final factored form. The final factored form of the expression is (3x-5)^(6) * (3x + 4).

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Factor completely:

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9(3 x-5)^{6}+(3 x-5)^{7}

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Answer:

Identify Common Factor: Identify the common factor in both terms. $\newline$ The expression given is $9(3x-5)^{6}+(3x-5)^{7}$ . Both terms have a common factor of $(3x-5)^{6}$ .
Factor Out Common Factor: Factor out the common factor from both terms. $\newline$ We can factor out $(3x-5)^{6}$ from both terms to simplify the expression. $\newline$ Factored Form: $(3x-5)^{6} \times [9 + (3x-5)]$
Simplify Inside Brackets: Simplify the expression inside the brackets. $\newline$ Now we simplify the expression inside the brackets by adding the constant term $9$ to the term $(3x-5)$ . $\newline$ Simplified Form: $(3x-5)^{6} \times (3x-5 + 9)$
Combine Like Terms: Combine like terms inside the brackets. $\newline$ Inside the brackets, we combine the like terms $3x$ and $-5 + 9$ . $\newline$ Combined Form: $(3x-5)^{6} \times (3x + 4)$
Write Final Form: Write the final factored form. $\newline$ The final factored form of the expression is $(3x-5)^{6} \times (3x + 4)$ .