Factor completely: (3x+4)(2x-3)+(5x+2)(2x-3)^(2) Answer:

Recognize common factor: Recognize the common factor in the given expression. The common factor in both terms is (2x-3). We can factor this out using the distributive property.Factor out common factor: Factor out the common factor (2x-3). The expression becomes (2x-3)[(3x+4) + (5x+2)(2x-3)].Expand second term: Expand the second term inside the brackets. We need to multiply (5x+2) by (2x-3) to simplify the expression inside the brackets. This is done by using the distributive property (FOIL method). (5x+2)(2x-3) = 5x(2x) + 5x(-3) + 2(2x) + 2(-3) = 10x^2 - 15x + 4x - 6.Combine like terms: Combine like terms in the expanded expression. Combine -15x and 4x to get -11x. So, (5x+2)(2x-3) = 10x^2 - 11x - 6.Substitute expanded expression: Substitute the expanded expression back into the factored form. The expression now reads (2x-3)[(3x+4) + (10x^2 - 11x - 6)].Distribute across terms: Distribute the (2x-3) across the terms inside the brackets. We need to add (3x+4) to (10x^2 - 11x - 6) before we can distribute (2x-3). (3x+4) + (10x^2 - 11x - 6) = 10x^2 - 8x - 2.Write final factored expression: Write the final factored expression. The completely factored form of the expression is (2x-3)(10x^2 - 8x - 2).

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Factor completely:

(3x+4)(2x-3)+(5x+2)(2x-3)^(2)
Answer:

Factor completely: $\newline$ $(3 x+4)(2 x-3)+(5 x+2)(2 x-3)^{2}$ $\newline$ Answer:

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

Full solution

Q. Factor completely:

\newline

(3 x+4)(2 x-3)+(5 x+2)(2 x-3)^{2}

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Answer:

Recognize common factor: Recognize the common factor in the given expression. $\newline$ The common factor in both terms is $(2x-3)$ . We can factor this out using the distributive property.
Factor out common factor: Factor out the common factor $(2x-3)$ . $\newline$ The expression becomes $(2x-3)[(3x+4) + (5x+2)(2x-3)]$ .
Expand second term: Expand the second term inside the brackets. $\newline$ We need to multiply $(5x+2)$ by $(2x-3)$ to simplify the expression inside the brackets. This is done by using the distributive property (FOIL method). $\newline$ $(5x+2)(2x-3) = 5x(2x) + 5x(-3) + 2(2x) + 2(-3) = 10x^2 - 15x + 4x - 6$ .
Combine like terms: Combine like terms in the expanded expression. $\newline$ Combine $-15x$ and $4x$ to get $-11x$ . $\newline$ So, $(5x+2)(2x-3) = 10x^2 - 11x - 6$ .
Substitute expanded expression: Substitute the expanded expression back into the factored form. $\newline$ The expression now reads $(2x-3)[(3x+4) + (10x^2 - 11x - 6)]$ .
Distribute across terms: Distribute the $(2x-3)$ across the terms inside the brackets. $\newline$ We need to add $(3x+4)$ to $(10x^2 - 11x - 6)$ before we can distribute $(2x-3)$ . $\newline$ $(3x+4) + (10x^2 - 11x - 6) = 10x^2 - 8x - 2$ .
Write final factored expression: Write the final factored expression. $\newline$ The completely factored form of the expression is $(2x-3)(10x^2 - 8x - 2)$ .