Factor completely: (6x-7)^(2)-(x+4)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. A difference of squares is a mathematical expression of the form a² - b², which can be factored into (a - b)(a + b).Identify 'a' and 'b': Identify 'a' and 'b' in the expression (6x-7)² - (x+4)². Here, 'a' is (6x-7) and 'b' is (x+4).Apply formula to factor: Apply the difference of squares formula to factor the expression. Using the formula (a² - b²) = (a - b)(a + b), we get: (6x-7)² - (x+4)² = (6x-7 - (x+4))(6x-7 + (x+4))Simplify factored expression: Simplify the factored expression. Now we simplify each part: (6x-7 - x - 4) = (5x - 11) (6x-7 + x + 4) = (7x - 3) So, the factored expression is (5x - 11)(7x - 3).

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Factor completely:

(6x-7)^(2)-(x+4)^(2)
Answer:

Factor completely: $\newline$ $(6 x-7)^{2}-(x+4)^{2}$ $\newline$ Answer:

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

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Q. Factor completely:

\newline

(6 x-7)^{2}-(x+4)^{2}

\newline

Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. A difference of squares is a mathematical expression of the form $a^2 - b^2$ , which can be factored into $(a - b)(a + b)$ .
Identify 'a' and 'b': Identify 'a' and 'b' in the expression $(6x-7)^2 - (x+4)^2$ . Here, 'a' is $(6x-7)$ and 'b' is $(x+4)$ .
Apply formula to factor: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $(a^2 - b^2) = (a - b)(a + b)$ , we get: $\newline$ $(6x-7)^2 - (x+4)^2 = (6x-7 - (x+4))(6x-7 + (x+4))$
Simplify factored expression: Simplify the factored expression. $\newline$ Now we simplify each part: $\newline$ $(6x-7 - x - 4) = (5x - 11)$ $\newline$ $(6x-7 + x + 4) = (7x - 3)$ $\newline$ So, the factored expression is $(5x - 11)(7x - 3)$ .