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

Identify Common Factor: Identify the common factor in both terms. The expression given is 6(x-3)^(5)-(x-3)^(6). Both terms have a common factor of (x-3)^(5).Factor Out Common Factor: Factor out the common factor of (x-3)^(5). We can write the expression as (x-3)^(5) * [6 - (x-3)].Simplify Inside Brackets: Simplify the expression inside the brackets. Subtract (x-3) from 6, which gives us 6 - x + 3.Combine Like Terms: Combine like terms inside the brackets. Adding 6 and 3 gives us 9, so the expression inside the brackets becomes 9 - x.Write Final Factored Form: Write the final factored form. The completely factored form of the expression is (x-3)^(5) * (9 - x).

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Factor completely:

6(x-3)^(5)-(x-3)^(6)
Answer:

Factor completely: $\newline$ $6(x-3)^{5}-(x-3)^{6}$ $\newline$ Answer:

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Factor completely:

\newline

6(x-3)^{5}-(x-3)^{6}

\newline

Answer:

Identify Common Factor: Identify the common factor in both terms. $\newline$ The expression given is $6(x-3)^{5}-(x-3)^{6}$ . Both terms have a common factor of $(x-3)^{5}$ .
Factor Out Common Factor: Factor out the common factor of $(x-3)^{5}$ . We can write the expression as $(x-3)^{5} \times [6 - (x-3)]$ .
Simplify Inside Brackets: Simplify the expression inside the brackets. $\newline$ Subtract $(x-3)$ from $6$ , which gives us $6 - x + 3$ .
Combine Like Terms: Combine like terms inside the brackets. $\newline$ Adding $6$ and $3$ gives us $9$ , so the expression inside the brackets becomes $9 - x$ .
Write Final Factored Form: Write the final factored form. $\newline$ The completely factored form of the expression is $(x-3)^{5} \times (9 - x)$ .