Factor completely. 49c^(2)+70 cd+25d^(2)=

Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic trinomial. Step Calculation: Coefficients are 49, 70, 25. Step Output: Coefficients: 49, 70, 25Recognize Pattern: Step Title: Recognize the Pattern Concise Step Description: Recognize that the quadratic trinomial is a perfect square trinomial. Step Calculation: Check if the first term is a perfect square, the last term is a perfect square, and if twice the product of the square roots of the first and last terms equals the middle term. Step Output: $49c^2$ is a perfect square of $7c$, $25d^2$ is a perfect square of $5d$, and $2 \times 7c \times 5d = 70cd$.Write Factored Form: Step Title: Write the Factored Form Concise Step Description: Write the factored form of the quadratic trinomial as the square of a binomial. Step Calculation: The factored form is $(7c + 5d)^2$. Step Output: Factored Form: $(7c + 5d)^2$

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Math Problems

Algebra 2

Factor polynomials

Full solution

Q. Factor completely.

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49 c^{2}+70 c d+25 d^{2}=

Identify Coefficients: Step Title: Identify the Coefficients $\newline$ Concise Step Description: Identify the coefficients of the quadratic trinomial. $\newline$ Step Calculation: Coefficients are $49$ , $70$ , $25$ . $\newline$ Step Output: Coefficients: $49$ , $70$ , $25$
Recognize Pattern: Step Title: Recognize the Pattern $\newline$ Concise Step Description: Recognize that the quadratic trinomial is a perfect square trinomial. $\newline$ Step Calculation: Check if the first term is a perfect square, the last term is a perfect square, and if twice the product of the square roots of the first and last terms equals the middle term. $\newline$ Step Output: $49c^2$ is a perfect square of $7c$ , $25d^2$ is a perfect square of $5d$ , and $2 \times 7c \times 5d = 70cd$ .
Write Factored Form: Step Title: Write the Factored Form $\newline$ Concise Step Description: Write the factored form of the quadratic trinomial as the square of a binomial. $\newline$ Step Calculation: The factored form is $(7c + 5d)^2$ . $\newline$ Step Output: Factored Form: $(7c + 5d)^2$