Chapter 4 - Polynomials - 4.5 Multiplication of Polynomials - 4.5 Exercise Set - Page 269: 51

$\dfrac{3}{16}a^2+\dfrac{5}{4}a-2$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $\left( \dfrac{1}{4}a+2 \right)\left( \dfrac{3}{4}a-1 \right)$, is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{4}a\left( \dfrac{3}{4}a \right)+\dfrac{1}{4}a(-1)+2\left( \dfrac{3}{4}a \right)+2(-1) \\\\= \dfrac{3}{16}a^2-\dfrac{1}{4}a+\dfrac{6}{4}a-2 \\\\= \dfrac{3}{16}a^2+\dfrac{5}{4}a-2 .\end{array}

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