Factor completely: (x-2)^(2)-(10 x+7)^(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-2)² is our 'a²' and (10x+7)² is our 'b²'.Apply formula: Apply the difference of squares formula. Using the formula (a² - b²) = (a - b)(a + b), we can write: (x-2)² - (10x+7)² = [(x-2) - (10x+7)][(x-2) + (10x+7)].Simplify expressions: Simplify the expressions inside the brackets. First bracket: (x-2) - (10x+7) = x - 2 - 10x - 7 = -9x - 9. Second bracket: (x-2) + (10x+7) = x - 2 + 10x + 7 = 11x + 5.Write factored form: Write the factored form using the simplified expressions. The factored form of the expression is (-9x - 9)(11x + 5).

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Factor completely:

(x-2)^(2)-(10 x+7)^(2)
Answer:

Factor completely: $\newline$ $(x-2)^{2}-(10 x+7)^{2}$ $\newline$ 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-2)^{2}-(10 x+7)^{2}

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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, $(x-2)^2$ is our ' $a^2$ ' and $(10x+7)^2$ is our ' $b^2$ '.
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula $(a^2 - b^2) = (a - b)(a + b)$ , we can write: $\newline$ $(x-2)^2 - (10x+7)^2 = [(x-2) - (10x+7)][(x-2) + (10x+7)]$ .
Simplify expressions: Simplify the expressions inside the brackets. $\newline$ First bracket: $(x-2) - (10x+7) = x - 2 - 10x - 7 = -9x - 9$ . $\newline$ Second bracket: $(x-2) + (10x+7) = x - 2 + 10x + 7 = 11x + 5$ .
Write factored form: Write the factored form using the simplified expressions. $\newline$ The factored form of the expression is $(-9x - 9)(11x + 5)$ .