If b = 5, determine the value of an expression (5/b+5b)(25/(b²)-25+25b²) using an identity.

If b = 5, determine the value of an expression…

If b = 5, determine the value of an expression $\left(\frac{5}{b}+5b\right)\left(\frac{25}{b^2}-25+25b^2\right)$ using an identity.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 15626.

We know that

x³ + y³ = (x + y)(x² + y² - xy)

Let x = $\frac{5}{b}$ and y = 5b

Substituting the values we get

( $\frac{5}{b}$ )³+ (5b)³ = $\left(\frac{5}{b}+5b\right)\left(\frac{25}{b^2}-25+25b^2\right)$

⇒ $\left(\frac{5}{b}+5b\right)\left(\frac{25}{b^2}-25+25b^2\right)$ = ( $\frac{5}{5}$ )³ + (5 × 5)³ = 1 + 15625 = 15626