Question

Multiply using a special product formula. (5x-9)(5x+9)

Answer 1

• Answer:

`\Large{\boxed{\sf (5x - 9)(5x + 9) = 25x^2 - 81}}`

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• Explanation:

To expand the given expression, we will apply the following special product formula, known as the difference of two squares:

`\red{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \red{ \star \: \sf{\boxed{ \sf Difference \ of \ two \ squares \text{:}}}} \\ \\ \sf \diamond \: (a - b)(a + b) = a^2 - b^2 \\ \end{array}}\\\end{gathered} \end{gathered}}`

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Given expression:

`\sf (5x - 9)(5x + 9)`

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Let a = 5x and b = 9.

`\rightarrow \sf (5x - 9)(5x + 9) = (5x)^2 - 9^2 \\ \\ \sf = (5x)\ast(5x) - 9\ast 9 \\ \\ \\ \sf = \boxed{\boxed{\sf 25x^2 - 81}}`