Question

Please I'm in urgent need of help. what must be added to make (1/4)x^2-(2/3)xy a perfect square?.​

Answer 1

Answer:

$\bigg(\frac{2}{3} {y} \bigg)^{2}$

STEP BY STEP EXPLANATION

$\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy \\ \\ = \bigg(\frac{1}{2} {x} \bigg)^{2} - 2. \bigg(\frac{1}{2} {x} \bigg)\bigg( \frac{2}{3} y \bigg ) + \bigg(\frac{2}{3} {y} \bigg)^{2} \\ \\ = \bigg(\frac{1}{2} {x} - \frac{2}{3} y\bigg)^{2}$

To make $\red{\bold{\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy}}$ a perfect square we should add $\purple{\bold{\bigg(\frac{2}{3} {y} \bigg)^{2}}}$

Answer 2

Answer:

• $4/9y^2$

Step-by-step explanation:

Given:

• $(1/4)x^2-(2/3)xy$

Consider the identity:

• $(a - b)^2=a^2-2ab+b^2$

We can see that:

• $a^2=(1/2x)^2$
• $a = (1/2)x$
• $2ab = (2/3)xy$

We can work out the value of b:

• $2ab = (2/3)xy = 2(1/2x)(2/3y)$
• $b=(2/3)y$

Then we are missing b², what needs to be added:

• $b^2=(2/3y)^2=4/9y^2$