Question
Write the following squares of binomials as trinomials:
$\big(\frac{\text{x}}{4}−\frac{\text{y}}{3}\big)^2$
$\big(\frac{\text{x}}{4}−\frac{\text{y}}{3}\big)^2$
✓
Answer
We will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(\frac{\text{x}}{4}−\frac{\text{y}}{3}\big)^2$
$=\big(\frac{\text{x}}{4}\big)^2−2\big(\frac{\text{x}}{4}\big)\big(\frac{\text{y}}{3}\big)+\big(\frac{\text{y}}{3})^2$
$=\frac{\text{x}^2}{16}−\frac{1}{6}\text{xy}+\frac{\text{y}^2}{9}$
$\big(\frac{\text{x}}{4}−\frac{\text{y}}{3}\big)^2$
$=\big(\frac{\text{x}}{4}\big)^2−2\big(\frac{\text{x}}{4}\big)\big(\frac{\text{y}}{3}\big)+\big(\frac{\text{y}}{3})^2$
$=\frac{\text{x}^2}{16}−\frac{1}{6}\text{xy}+\frac{\text{y}^2}{9}$
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