Factor completely: (7x-2)^(2)-(3x-1)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The given expression is in the form of a^2 - b^2, which is a difference of squares. a = (7x-2) and b = (3x-1). Difference of squares formula: a^2 - b^2 = (a + b)(a - b).Apply formula: Apply the difference of squares formula. Using the formula from Step 1, we can write the expression as: (7x-2 + 3x-1)(7x-2 - (3x-1)).Simplify terms: Simplify the terms inside the parentheses. First, combine like terms in the first set of parentheses: (7x + 3x) - (2 + 1) = 10x - 3. Then, distribute the negative sign in the second set of parentheses: (7x - 2) - 3x + 1 = 4x - 1.Write factored form: Write the factored form using the simplified terms. The completely factored form of the expression is: (10x - 3)(4x - 1).

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Factor completely:

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(7 x-2)^{2}-(3 x-1)^{2}

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Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. $\newline$ The given expression is in the form of $a^2 - b^2$ , which is a difference of squares. $\newline$ $a = (7x-2)$ and $b = (3x-1)$ . $\newline$ Difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula from Step $1$ , we can write the expression as: $\newline$ $(7x^2 + 3x^1)(7x^2 - (3x^1))$ .
Simplify terms: Simplify the terms inside the parentheses. $\newline$ First, combine like terms in the first set of parentheses: $\newline$ $(7x + 3x) - (2 + 1) = 10x - 3$ . $\newline$ Then, distribute the negative sign in the second set of parentheses: $\newline$ $(7x - 2) - 3x + 1 = 4x - 1$ .
Write factored form: Write the factored form using the simplified terms. $\newline$ The completely factored form of the expression is: $\newline$ $(10x - 3)(4x - 1)$ .