Factor completely: (5x-1)^(2)(4x+5)+(x+7)(5x-1) Answer:

Identify common factors: Identify common factors in both terms of the expression. The expression is (5x-1)^(2)(4x+5)+(x+7)(5x-1). We can see that (5x-1) is a common factor in both terms.Factor out common factor: Factor out the common factor (5x-1). We can write the expression as (5x-1)[(5x-1)(4x+5)+(x+7)].Distribute common factor: Distribute the common factor (5x-1) in the second term. Now we have (5x-1)[(5x-1)(4x+5)+1(x+7)].Expand terms inside brackets: Expand the terms inside the brackets. We get (5x-1)[20x^2 + 25x - 4x - 5 + x + 7].Combine like terms: Combine like terms inside the brackets. This simplifies to (5x-1)[20x^2 + 22x + 2].Factor quadratic expression: Factor the quadratic expression inside the brackets if possible. The quadratic 20x^2 + 22x + 2 can be factored as (10x+1)(2x+2).Combine factored quadratic: Combine the factored quadratic with the common factor (5x-1). The completely factored expression is (5x-1)(10x+1)(2x+2).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor completely:

(5x-1)^(2)(4x+5)+(x+7)(5x-1)
Answer:

Factor completely: $\newline$ $(5 x-1)^{2}(4 x+5)+(x+7)(5 x-1)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Factor completely:

\newline

(5 x-1)^{2}(4 x+5)+(x+7)(5 x-1)

\newline

Answer:

Identify common factors: Identify common factors in both terms of the expression. $\newline$ The expression is $(5x-1)^{2}(4x+5)+(x+7)(5x-1)$ . We can see that $(5x-1)$ is a common factor in both terms.
Factor out common factor: Factor out the common factor $(5x-1)$ . We can write the expression as $(5x-1)[(5x-1)(4x+5)+(x+7)]$ .
Distribute common factor: Distribute the common factor $(5x-1)$ in the second term. $\newline$ Now we have $(5x-1)[(5x-1)(4x+5)+1(x+7)]$ .
Expand terms inside brackets: Expand the terms inside the brackets. $\newline$ We get $(5x-1)[20x^2 + 25x - 4x - 5 + x + 7]$ .
Combine like terms: Combine like terms inside the brackets. $\newline$ This simplifies to $(5x-1)[20x^2 + 22x + 2]$ .
Factor quadratic expression: Factor the quadratic expression inside the brackets if possible. $\newline$ The quadratic $20x^2 + 22x + 2$ can be factored as $(10x+1)(2x+2)$ .
Combine factored quadratic: Combine the factored quadratic with the common factor $(5x-1)$ . $\newline$ The completely factored expression is $(5x-1)(10x+1)(2x+2)$ .