Question
Write the following squares of binomials as trinomials:
$\big(\frac{3\text{a}}{2}−\frac{5\text{b}}{4}\big)^2$
$\big(\frac{3\text{a}}{2}−\frac{5\text{b}}{4}\big)^2$
✓
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.
$\big(\frac{3\text{a}}{2}−\frac{5\text{b}}{4}\big)^2$
$=\big(\frac{3\text{a}}{2}\big)^2−2\big(\frac{3\text{a}}{2}\big)\big(\frac{5\text{b}}{4}\big)+\big(\frac{5\text{b}}{4}\big)^2$
$=\frac{9\text{a}^2}{4}−\frac{15\text{ab}}{4}+\frac{25\text{b}^2}{16}$
$\big(\frac{3\text{a}}{2}−\frac{5\text{b}}{4}\big)^2$
$=\big(\frac{3\text{a}}{2}\big)^2−2\big(\frac{3\text{a}}{2}\big)\big(\frac{5\text{b}}{4}\big)+\big(\frac{5\text{b}}{4}\big)^2$
$=\frac{9\text{a}^2}{4}−\frac{15\text{ab}}{4}+\frac{25\text{b}^2}{16}$
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