Factor completely: (3x+5)^(2)(2x+7)+(3x-7)(3x+5) Answer:

Identify common factors: Identify common factors in both terms. The expression has two terms: (3x+5)^(2)(2x+7) and (3x-7)(3x+5). The common factor in both terms is (3x+5).Factor out common factor: Factor out the common factor (3x+5). We can write the expression as (3x+5)[(3x+5)(2x+7) + (3x-7)].Distribute and simplify: Distribute (3x+5) in the first term and simplify the expression inside the brackets. (3x+5)[(3x+5)(2x+7) + (3x-7)] becomes (3x+5)[6x^2 + 21x + 10x + 35 + 3x - 7].Combine like terms: Combine like terms inside the brackets. (3x+5)[6x^2 + 21x + 10x + 35 + 3x - 7] simplifies to (3x+5)(6x^2 + 34x + 28).Factor quadratic expression: Factor the quadratic expression inside the brackets if possible. The quadratic expression 6x^2 + 34x + 28 can be factored as 2(3x^2 + 17x + 14).Factor quadratic expression: Factor the quadratic expression 3x^2 + 17x + 14. We look for two numbers that multiply to 3*14=42 and add up to 17. These numbers are 2 and 21. So, 3x^2 + 17x + 14 can be factored as (3x+2)(x+7).Write final factored form: Write the final factored form of the original expression. The final factored form is (3x+5) * 2 * (3x+2)(x+7).

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Factor completely:

(3x+5)^(2)(2x+7)+(3x-7)(3x+5)
Answer:

Factor completely: $\newline$ $(3 x+5)^{2}(2 x+7)+(3 x-7)(3 x+5)$ $\newline$ Answer:

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Q. Factor completely:

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(3 x+5)^{2}(2 x+7)+(3 x-7)(3 x+5)

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Answer:

Identify common factors: Identify common factors in both terms. $\newline$ The expression has two terms: \(3x+ $5$ )^{ $2$ }( $2$ x+ $7$ )\ and \(3x $-7$ )( $3$ x+ $5$ )\. The common factor in both terms is \(3x+ $5$ )\.
Factor out common factor: Factor out the common factor $(3x+5)$ . We can write the expression as $(3x+5)[(3x+5)(2x+7) + (3x-7)]$ .
Distribute and simplify: Distribute $(3x+5)$ in the first term and simplify the expression inside the brackets. $(3x+5)[(3x+5)(2x+7) + (3x-7)]$ becomes $(3x+5)[6x^2 + 21x + 10x + 35 + 3x - 7]$ .
Combine like terms: Combine like terms inside the brackets. $\newline$ $(3x+5)[6x^2 + 21x + 10x + 35 + 3x - 7]$ simplifies to $(3x+5)(6x^2 + 34x + 28)$ .
Factor quadratic expression: Factor the quadratic expression inside the brackets if possible. $\newline$ The quadratic expression $6x^2 + 34x + 28$ can be factored as $2(3x^2 + 17x + 14)$ .
Factor quadratic expression: Factor the quadratic expression $3x^2 + 17x + 14$ . We look for two numbers that multiply to $3\times14=42$ and add up to $17$ . These numbers are $2$ and $21$ . So, $3x^2 + 17x + 14$ can be factored as $(3x+2)(x+7)$ .
Write final factored form: Write the final factored form of the original expression. $\newline$ The final factored form is $(3x+5) \times 2 \times (3x+2)(x+7)$ .