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

Recognize: 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. The difference of squares can be factored into (a + b)(a - b). Here, a = (3x - 2) and b = (10x - 7).Apply formula: Apply the difference of squares formula. Using the formula (a + b)(a - b) to factor the expression, we get: ((3x - 2) + (10x - 7))((3x - 2) - (10x - 7))Simplify factors: Simplify each factor. Simplify the first factor: (3x - 2) + (10x - 7) = 3x + 10x - 2 - 7 = 13x - 9 Simplify the second factor: (3x - 2) - (10x - 7) = 3x - 10x - 2 + 7 = -7x + 5Write factored form: Write the factored form of the expression. The completely factored form of the expression is: (13x - 9)(-7x + 5)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor completely:

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

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

View step-by-step help

Home

Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Factor completely:

\newline

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

\newline

Answer:

Recognize: 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. $\newline$ The difference of squares can be factored into $(a + b)(a - b)$ . $\newline$ Here, $a = (3x - 2)$ and $b = (10x - 7)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula $(a + b)(a - b)$ to factor the expression, we get: $\newline$ $((3x - 2) + (10x - 7))((3x - 2) - (10x - 7))$
Simplify factors: Simplify each factor. $\newline$ Simplify the first factor: $\newline$ $(3x - 2) + (10x - 7) = 3x + 10x - 2 - 7 = 13x - 9$ $\newline$ Simplify the second factor: $\newline$ $(3x - 2) - (10x - 7) = 3x - 10x - 2 + 7 = -7x + 5$
Write factored form: Write the factored form of the expression. $\newline$ The completely factored form of the expression is: $\newline$ $(13x - 9)(-7x + 5)$