Question

difference of perfect squares (level 1)
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question
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factor completely.
49 - 100x²

Explanation:

Step1: Identify the difference of squares

The expression \(49 - 100x^2\) is a difference of perfect squares. Recall the formula for the difference of squares: \(a^2 - b^2=(a + b)(a - b)\). Here, \(a^2 = 49\) and \(b^2=100x^2\).

Step2: Find \(a\) and \(b\)

For \(a^2 = 49\), we take the square root of 49, so \(a = 7\) (since \(7^2=49\)). For \(b^2 = 100x^2\), we take the square root of \(100x^2\), so \(b = 10x\) (since \((10x)^2=100x^2\)).

Step3: Apply the difference of squares formula

Substitute \(a = 7\) and \(b = 10x\) into the formula \(a^2 - b^2=(a + b)(a - b)\). So \(49 - 100x^2=(7 + 10x)(7 - 10x)\).

Answer:

\((7 + 10x)(7 - 10x)\)