Factor completely: (x-4)(4x-7)-(x-4)^(2)(x-8) Answer:

Identify common factors: Identify common factors in the given expression. The expression has (x-4) as a common factor in both terms.Factor out common factor: Factor out the common factor (x-4) from the expression. We can write the expression as (x-4)[(4x-7) - (x-4)(x-8)].Distribute and simplify: Distribute the negative sign and simplify the expression inside the brackets. This gives us (x-4)[4x - 7 - (x^2 - 8x + 4x - 32)].Combine like terms: Combine like terms inside the brackets. This simplifies to (x-4)[4x - 7 - x^2 + 4x - 32].Continue simplifying: Continue simplifying the expression inside the brackets. Combine the x terms to get (x-4)[-x^2 + 8x - 7 - 32].Combine constant terms: Combine the constant terms inside the brackets. This results in (x-4)[-x^2 + 8x - 39].Final factored form: Since we cannot factor the quadratic expression further, we have the final factored form. The completely factored form of the expression is (x-4)(-x^2 + 8x - 39).

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Factor completely:

(x-4)(4x-7)-(x-4)^(2)(x-8)
Answer:

Factor completely: $\newline$ $(x-4)(4 x-7)-(x-4)^{2}(x-8)$ $\newline$ Answer:

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

Full solution

Q. Factor completely:

\newline

(x-4)(4 x-7)-(x-4)^{2}(x-8)

\newline

Answer:

Identify common factors: Identify common factors in the given expression. $\newline$ The expression has $(x-4)$ as a common factor in both terms.
Factor out common factor: Factor out the common factor $(x-4)$ from the expression. $\newline$ We can write the expression as $(x-4)[(4x-7) - (x-4)(x-8)].$
Distribute and simplify: Distribute the negative sign and simplify the expression inside the brackets. $\newline$ This gives us $(x-4)[4x - 7 - (x^2 - 8x + 4x - 32)]$ .
Combine like terms: Combine like terms inside the brackets. $\newline$ This simplifies to $(x-4)[4x - 7 - x^2 + 4x - 32]$ .
Continue simplifying: Continue simplifying the expression inside the brackets. $\newline$ Combine the $x$ terms to get $(x-4)[-x^2 + 8x - 7 - 32]$ .
Combine constant terms: Combine the constant terms inside the brackets. $\newline$ This results in $(x-4)[-x^2 + 8x - 39]$ .
Final factored form: Since we cannot factor the quadratic expression further, we have the final factored form. The completely factored form of the expression is $(x-4)(-x^2 + 8x - 39)$ .