Exponents and Polynomials
Factoring a difference of squares in one variable: Advanced

Factor.
\[
49-4 u^{2}
\]

Answer

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Answer

\(\boxed{-(2u - 7)(2u + 7)}\) is the final answer.

Steps

Step 1 ：The given expression is a difference of squares. The difference of squares is a special case in algebra where \(a^{2} - b^{2}\) can be factored into \((a+b)(a-b)\). In this case, \(a^{2}\) is 49 and \(b^{2}\) is \(4u^{2}\). Therefore, a is 7 and b is 2u.

Step 2 ：We can substitute these values into the difference of squares formula to factor the expression.

Step 3 ：The factored form of the expression \(49 - 4u^{2}\) is \(-(2u - 7)(2u + 7)\).

Step 4 ：\(\boxed{-(2u - 7)(2u + 7)}\) is the final answer.

Exponents and PolynomialsFactoring a difference of squares in one variable: Advanced Factor.\[49-4 u^{2}\]

Answer

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Exponents and Polynomials
Factoring a difference of squares in one variable: Advanced

Factor.
\[
49-4 u^{2}
\]