Factor completely: (x+4)^(2)-(9x+1)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. A difference of squares is an algebraic expression of the form a² - b², which can be factored into (a + b)(a - b). Here, (x+4)² is a² and (9x+1)² is b².Apply formula: Apply the difference of squares formula. Using the formula, we can write the expression as: ((x+4) + (9x+1))((x+4) - (9x+1))Simplify each factor: Simplify each factor. First factor: (x+4) + (9x+1) = x + 4 + 9x + 1 = 10x + 5 Second factor: (x+4) - (9x+1) = x + 4 - 9x - 1 = -8x + 3Write final factored form: Write the final factored form. The completely factored form of the expression is (10x + 5)(-8x + 3).

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Factor completely:

(x+4)^(2)-(9x+1)^(2)
Answer:

Factor completely: $\newline$ $(x+4)^{2}-(9 x+1)^{2}$ $\newline$ 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)^{2}-(9 x+1)^{2}

\newline

Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. A difference of squares is an algebraic expression of the form $a^2 - b^2$ , which can be factored into $(a + b)(a - b)$ . Here, $(x+4)^2$ is $a^2$ and $(9x+1)^2$ is $b^2$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula, we can write the expression as: $\newline$ $(x+4) + (9x+1))((x+4) - (9x+1))$
Simplify each factor: Simplify each factor. $\newline$ First factor: $(x+4) + (9x+1) = x + 4 + 9x + 1 = 10x + 5$ $\newline$ Second factor: $(x+4) - (9x+1) = x + 4 - 9x - 1 = -8x + 3$
Write final factored form: Write the final factored form. $\newline$ The completely factored form of the expression is $(10x + 5)(-8x + 3)$ .