Question

Factorize
16a^2 - 25/4a^2

Answer 1

$16 {a}^{2} - \frac{25}{4 {a}^{2} } \\ \\ = > (4a) {}^{2} -( \frac{5}{2a} ) {}^{2} \\ \\ = > (4a - \frac{5}{2a} )(4a + \frac{5}{2a} )$

Answer 2

The required factorised form is $(4a-\dfrac{5}{2a})(4a+\dfrac{5}{2a})$

Step-by-step explanation:

Since we have given that

$16a^2-\dfrac{25}{4a^2}$

We need to factorise the above expression:

As we know that

$a^2-b^2=(a-b)(a+b)$

So, using this, we get that

$16a^2-\dfrac{25}{4a^2}\\\\=(4a)^2-(\dfrac{5}{2a})^2\\\\=(4a-\dfrac{5}{2a})(4a+\dfrac{5}{2a})$

Hence, the required factorised form is $(4a-\dfrac{5}{2a})(4a+\dfrac{5}{2a})$

# learn more:

Factorise: 16a^2 - 25÷ 4a^2​

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