The expression given is 49p² − 4q². We need to factor this expression. Step 1: Recognize the form of the expression. The expression 49p² − 4q² is a difference of squares, which follows the algebraic identity a² − b² = (a−b)(a+b). Step 2: Identify a and b. For a² = 49p², we find a by taking the square root: a = √(49p²) = 7p. For b² = 4q², we find b by taking the square root: b = √(4q²) = 2q. Step 3: Apply the difference of squares formula. Substitute a = 7p and b = 2q into the formula (a−b)(a+b). 49p² − 4q² = (7p − 2q)(7p + 2q) The completely factored form of the expression is: (7p − 2q)(7p + 2q)

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49p2 - 4q2

June 2, 2026Mathematics

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Answer

(7p - 2q)(7p + 2q)

Step-by-step solution

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The expression given is $49p^2 - 4q^2$ . We need to factor this expression.

Recognize the form of the expression.
The expression $49p^2 - 4q^2$ is a difference of squares, which follows the algebraic identity $a^2 - b^2 = (a-b)(a+b)$ .
Identify $a$ and $b$ .
For $a^2 = 49p^2$ , we find $a$ by taking the square root: $a = \sqrt{49p^2} = 7p$ .
For $b^2 = 4q^2$ , we find $b$ by taking the square root: $b = \sqrt{4q^2} = 2q$ .
Apply the difference of squares formula.
Substitute $a = 7p$ and $b = 2q$ into the formula $(a-b)(a+b)$ .
$49p^2 - 4q^2 = (7p - 2q)(7p + 2q)$
The completely factored form of the expression is:
$(7p - 2q)(7p + 2q)$

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49p2 - 4q2

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Step-by-step solution

Recognize the form of the expression.

Identify aaa and bbb.

Apply the difference of squares formula.

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