Factor completely: (x+4)(5x-9)+(4x-7)(x+4) Answer:

Distribute Terms in Parentheses: Distribute the terms within each set of parentheses. We will apply the distributive property (a(b + c) = ab + ac) to both (x+4)(5x-9) and (4x-7)(x+4). First, for (x+4)(5x-9): 5x(x) + 5x(-9) + 4(5x) + 4(-9) = 5x^2 - 45x + 20x - 36 = 5x^2 - 25x - 36Distribute Terms for Expressions: Now, distribute the terms for (4x-7)(x+4): 4x(x) + 4x(4) - 7(x) - 7(4) = 4x^2 + 16x - 7x - 28 = 4x^2 + 9x - 28Combine Like Terms: Add the results from Step 1 and Step 2. We combine like terms from the expressions 5x^2 - 25x - 36 and 4x^2 + 9x - 28. (5x^2 - 25x - 36) + (4x^2 + 9x - 28) = 5x^2 + 4x^2 - 25x + 9x - 36 - 28 = 9x^2 - 16x - 64Factor by Grouping: Factor by grouping, if possible. Looking at the expression 9x^2 - 16x - 64, we can try to factor by grouping. However, since there are no common factors and the trinomial does not factor neatly, we cannot factor by grouping in this case.Factor Quadratic Expression: Factor the quadratic expression, if possible. We look for two numbers that multiply to (9)(-64) = -576 and add to -16. After checking possible factors, we find that there are no such integers that satisfy both conditions. Therefore, the quadratic expression 9x^2 - 16x - 64 cannot be factored further over the integers.

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Factor completely:

(x+4)(5x-9)+(4x-7)(x+4)
Answer:

Factor completely: $\newline$ $(x+4)(5 x-9)+(4 x-7)(x+4)$ $\newline$ Answer:

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

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Q. Factor completely:

\newline

(x+4)(5 x-9)+(4 x-7)(x+4)

\newline

Answer:

Distribute Terms in Parentheses: Distribute the terms within each set of parentheses. $\newline$ We will apply the distributive property $a(b + c) = ab + ac$ to both $(x+4)(5x-9)$ and $(4x-7)(x+4)$ . $\newline$ First, for $(x+4)(5x-9)$ : $\newline$ $5x(x) + 5x(-9) + 4(5x) + 4(-9)$ $\newline$ $= 5x^2 - 45x + 20x - 36$ $\newline$ $= 5x^2 - 25x - 36$
Distribute Terms for Expressions: Now, distribute the terms for $(4x-7)(x+4)$ : $4x(x) + 4x(4) - 7(x) - 7(4)$ $= 4x^2 + 16x - 7x - 28$ $= 4x^2 + 9x - 28$
Combine Like Terms: Add the results from Step $1$ and Step $2$ . $\newline$ We combine like terms from the expressions $5x^2 - 25x - 36$ and $4x^2 + 9x - 28$ . $\newline$ $(5x^2 - 25x - 36) + (4x^2 + 9x - 28)$ $\newline$ $= 5x^2 + 4x^2 - 25x + 9x - 36 - 28$ $\newline$ $= 9x^2 - 16x - 64$
Factor by Grouping: Factor by grouping, if possible. $\newline$ Looking at the expression $9x^2 - 16x - 64$ , we can try to factor by grouping. However, since there are no common factors and the trinomial does not factor neatly, we cannot factor by grouping in this case.
Factor Quadratic Expression: Factor the quadratic expression, if possible. $\newline$ We look for two numbers that multiply to $(9)(-64) = -576$ and add to $-16$ . After checking possible factors, we find that there are no such integers that satisfy both conditions. Therefore, the quadratic expression $9x^2 - 16x - 64$ cannot be factored further over the integers.