Question

12x^3 - 75xy^2 = ? *
3x(2x - 5y)^2
2x(2x + 5y)^2
3x(2x + 5y)(2x - 5y)​

Answer 1

$\underline{\bf{\sf{\red{Given}:-}}}$

• $\sf 12x^3 - 75xy^2$

We have to simplify this.

$\underline{\bf{\sf{\blue{Answer}:-}}}$

$\sf 12 {x}^{3} - 75x {y}^{2}$

Taking $\sf 3x$ as common,

$\longrightarrow \sf 3x(4 {x}^{2} - 25 {y}^{2} )$

Now,

$\sf 4x^2$ can be written as $\sf (2x)^2$, and $\sf 25y^2$ can be written as $\sf (5y)^2$.

So,

$\longrightarrow \sf 3x \bigg\{ {(2x)}^{2} - {(5y)}^{2} \bigg\}$

Now we have to use the formula,

${\blue{\bigstar}} \boxed{\sf{ a^2 - b^2 = (a + b)(a - b).}}$

Considering $\sf 2x$ as $\sf a$ and $\sf 5y$ as $\sf b,$

$\longrightarrow \sf 3x \bigg \{(2x + 5y)(2x - 5y) \bigg \}$

$\longrightarrow \sf 3x(2x + 5y)(2x - 5y)$

So, the simplified form is,

$\longrightarrow \underline{\underline{\sf{\green{3x(2x+5y)(2x-5y)}}}}$