Factor completely: (5x-6)(3x-5)-(3x-2)(3x-5) Answer:

Identify Common Factor: Identify the common factor in both terms. The common factor in both terms is (3x - 5).Factor Out Common Factor: Factor out the common factor (3x - 5). (5x-6)(3x-5)-(3x-2)(3x-5) = (3x - 5)((5x - 6) - (3x - 2))Simplify Inside Parentheses: Simplify the expression inside the parentheses. (5x - 6) - (3x - 2) = 5x - 6 - 3x + 2Combine Like Terms: Combine like terms. 5x - 6 - 3x + 2 = (5x - 3x) + (-6 + 2) = 2x - 4Write Factored Form: Write the factored form of the original expression. (3x - 5)(2x - 4)Check Further Factoring: Check if the expression (2x - 4) can be factored further. 2x - 4 can be factored as 2(x - 2).Write Completely Factored Form: Write the completely factored form of the original expression. (3x - 5)(2)(x - 2)

Home

Math Problems

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

Q. Factor completely:

\newline

(5 x-6)(3 x-5)-(3 x-2)(3 x-5)

\newline

Answer:

Identify Common Factor: Identify the common factor in both terms. $\newline$ The common factor in both terms is $(3x - 5)$ .
Factor Out Common Factor: Factor out the common factor $(3x - 5)$ . $\newline$ $(5x-6)(3x-5)-(3x-2)(3x-5) = (3x - 5)((5x - 6) - (3x - 2))$
Simplify Inside Parentheses: Simplify the expression inside the parentheses. $\newline$ $(5x - 6) - (3x - 2) = 5x - 6 - 3x + 2$
Combine Like Terms: Combine like terms. $\newline$ $5x - 6 - 3x + 2 = (5x - 3x) + (-6 + 2) = 2x - 4$
Write Factored Form: Write the factored form of the original expression. $\newline$ $(3x - 5)(2x - 4)$
Check Further Factoring: Check if the expression $(2x - 4)$ can be factored further. $2x - 4$ can be factored as $2(x - 2)$ .
Write Completely Factored Form: Write the completely factored form of the original expression. $\newline$ $(3x - 5)(2)(x - 2)$