Factor completely: (10 x-7)^(2)-(3x+2)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The expression (10x - 7)² - (3x + 2)² is a difference of two squares, which can be factored using the formula a² - b² = (a - b)(a + b).Identify 'a' and 'b': Identify 'a' and 'b' in the formula. In our case, 'a' is (10x - 7) and 'b' is (3x + 2).Apply formula: Apply the difference of squares formula. Using the formula from Step 1, we get: ((10x - 7) - (3x + 2))((10x - 7) + (3x + 2))Simplify expressions: Simplify the expressions inside the parentheses. First, we simplify (10x - 7) - (3x + 2), which gives us 10x - 7 - 3x - 2 = 7x - 9. Then, we simplify (10x - 7) + (3x + 2), which gives us 10x - 7 + 3x + 2 = 13x - 5.Write final factored form: Write the final factored form. The factored form of the expression is (7x - 9)(13x - 5).

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Factor completely:

(10 x-7)^(2)-(3x+2)^(2)
Answer:

Factor completely: $\newline$ $(10 x-7)^{2}-(3 x+2)^{2}$ $\newline$ Answer:

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

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Q. Factor completely:

\newline

(10 x-7)^{2}-(3 x+2)^{2}

\newline

Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The expression $(10x - 7)^2 - (3x + 2)^2$ is a difference of two squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify 'a' and 'b': Identify 'a' and 'b' in the formula. $\newline$ In our case, 'a' is $(10x - 7)$ and 'b' is $(3x + 2)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula from Step $1$ , we get: $\newline$ $((10x - 7) - (3x + 2))((10x - 7) + (3x + 2))$
Simplify expressions: Simplify the expressions inside the parentheses. $\newline$ First, we simplify $(10x - 7) - (3x + 2)$ , which gives us $10x - 7 - 3x - 2 = 7x - 9$ . $\newline$ Then, we simplify $(10x - 7) + (3x + 2)$ , which gives us $10x - 7 + 3x + 2 = 13x - 5$ .
Write final factored form: Write the final factored form. $\newline$ The factored form of the expression is $(7x - 9)(13x - 5)$ .