Factor completely. 4p^(2)-25q^(2)=

Recognize the form: Recognize the form of the expression. The expression 4p^2 - 25q^2 is a difference of squares because it can be written as (2p)^2 - (5q)^2.Apply the formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a + b)(a - b). Here, a is 2p and b is 5q.Substitute into formula: Substitute a and b into the formula. Using the values of a and b, we get (2p + 5q)(2p - 5q).Write final factorized form: Write the final factorized form. The expression 4p^2 - 25q^2 is fully factorized as (2p + 5q)(2p - 5q).

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Factor completely. $\newline$ $4 p^{2}-25 q^{2}=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Factor completely.

\newline

4 p^{2}-25 q^{2}=

Recognize the form: Recognize the form of the expression. $\newline$ The expression $4p^2 - 25q^2$ is a difference of squares because it can be written as $(2p)^2 - (5q)^2$ .
Apply the formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ . Here, $a$ is $2p$ and $b$ is $5q$ .
Substitute into formula: Substitute $a$ and $b$ into the formula. $\newline$ Using the values of $a$ and $b$ , we get $(2p + 5q)(2p - 5q)$ .
Write final factorized form: Write the final factorized form. $\newline$ The expression $4p^2 - 25q^2$ is fully factorized as $(2p + 5q)(2p - 5q)$ .