Question
Expand (i) (a + ab – 3b2) (4 + b), and (ii) (4y + 7) (y + 11z – 3).
✓
Answer
$\text { (i) }\left(a+a b-3 b^2\right)(4+b)$
$\begin{array}{l}=\left(a+a b-3 b^2\right) 4+\left(a+a b-3 b^2\right) b \\=4 a+4 a b-12 b^2+a b+a b^2-3 b^3 \\=-3 b^3-12 b^2+a b^2+4 a b+a b+4 a \\=-3 b^3-12 b^2+a b^2+5 a b+4 a\end{array}$
$\begin{array}{l}\text { (ii) }(4 y+7)(y+11 z-3) \\=(4 y+7) y+(4 y+7) 11 z-(4 y+7) 3 \\=4 y^2+7 y+44 y z+77 z-(12 y+21) \\=4 y^2+7 y+44 y z+77 z-12 y-21 \\=4 y^2+7 y-12 y+44 y z+77 z-21 \\=4 y^2-5 y+44 y z+77 z-21 .\end{array}$
$\begin{array}{l}=\left(a+a b-3 b^2\right) 4+\left(a+a b-3 b^2\right) b \\=4 a+4 a b-12 b^2+a b+a b^2-3 b^3 \\=-3 b^3-12 b^2+a b^2+4 a b+a b+4 a \\=-3 b^3-12 b^2+a b^2+5 a b+4 a\end{array}$
$\begin{array}{l}\text { (ii) }(4 y+7)(y+11 z-3) \\=(4 y+7) y+(4 y+7) 11 z-(4 y+7) 3 \\=4 y^2+7 y+44 y z+77 z-(12 y+21) \\=4 y^2+7 y+44 y z+77 z-12 y-21 \\=4 y^2+7 y-12 y+44 y z+77 z-21 \\=4 y^2-5 y+44 y z+77 z-21 .\end{array}$
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