Question

factorise 18x square - 32y square​

Answer 1

Step-by-step explanation:

→What is the largest number that divides evenly into $18{x}^{2}$ and $-32{y}^{2}?$

It is 2.

→ What is the highest degree of x that divides evenly into $18{x}^{2}$ and $-32{y}^{2}$

It is 1, since xx is not in every term.

→ What is the highest degree of y that divides evenly into $18{x}^{2}$ and $-32{y}^{2}$

It is 1, since yy is not in every term.

→ Multiplying the results above,

The GCF is 2.

→Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

$\tt \color{red} \implies2 \bigg(\dfrac{18{x}^{2}}{2}+\dfrac{-32{y}^{2}}{2} \bigg)$

→Simplify each term in parentheses.

$\tt \color{darkblue} \implies2(9{x}^{2}-16{y}^{2})$

Rewrite $\tt 9{x}^{2}-16{y}^{2}$in the form $\tt{a}^{2}-{b}^{2}$ , where a=3x and b=4y.

$\color{maroon} \implies \tt2 \bigg({(3x)}^{2}-{(4y)}^{2} \bigg)$

Use Difference of Squares: $\tt{a}^{2}-{b}^{2}$=(a+b)(a-b)

$\tt \pink{ \implies{2(3x+4y)(3x−4y)}}$