Factor completely: (3x+2)^(2)(3x-8)+(3x+2)(3x+10) Answer:

Identify Common Factors: Step Title: Identify Common Factors Concise Step Description: Look for common factors in each term of the expression. Step Calculation: The common factor in both terms is (3x+2). Step Output: Common factor: (3x+2)Factor Out Common Factor: Step Title: Factor Out the Common Factor Concise Step Description: Factor out the common factor (3x+2) from the expression. Step Calculation: Factoring out (3x+2) gives us (3x+2)[(3x+2)(3x-8)+(3x+10)]. Step Output: Factored expression: (3x+2)[(3x+2)(3x-8)+(3x+10)]Distribute and Combine Terms: Step Title: Distribute and Combine Like Terms Concise Step Description: Distribute the (3x+2) term across the expression inside the brackets and combine like terms. Step Calculation: Distributing gives us (3x+2)[(3x+2)(3x-8)+1(3x+10)]. Expanding the terms inside the brackets gives us (3x+2)(9x^2 - 24x + 6x - 16 + 3x + 10). Step Output: Expanded expression: (3x+2)(9x^2 - 15x - 6)

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Q. Factor completely:

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(3 x+2)^{2}(3 x-8)+(3 x+2)(3 x+10)

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Answer:

Identify Common Factors: Step Title: Identify Common Factors $\newline$ Concise Step Description: Look for common factors in each term of the expression. $\newline$ Step Calculation: The common factor in both terms is $(3x+2)$ . $\newline$ Step Output: Common factor: $(3x+2)$
Factor Out Common Factor: Step Title: Factor Out the Common Factor $\newline$ Concise Step Description: Factor out the common factor $(3x+2)$ from the expression. $\newline$ Step Calculation: Factoring out $(3x+2)$ gives us $(3x+2)[(3x+2)(3x-8)+(3x+10)]$ . $\newline$ Step Output: Factored expression: $(3x+2)[(3x+2)(3x-8)+(3x+10)]$
Distribute and Combine Terms: Step Title: Distribute and Combine Like Terms $\newline$ Concise Step Description: Distribute the $(3x+2)$ term across the expression inside the brackets and combine like terms. $\newline$ Step Calculation: Distributing gives us $(3x+2)[(3x+2)(3x-8)+1(3x+10)]$ . Expanding the terms inside the brackets gives us $(3x+2)(9x^2 - 24x + 6x - 16 + 3x + 10)$ . $\newline$ Step Output: Expanded expression: $(3x+2)(9x^2 - 15x - 6)$