Question 1: Multiply:

1. ${8x}^2\times{}\left(-5x\right)=-40x^3$
2. $\frac{2}{3}ab\times{}\left(-6a^2b\right)=-{4a}^3b^2$
3. ${7x}^2y^3\times{}\left(-4x^3y\right)=-28x^5y^4$
4. $(\frac{-5}{9}{ax}^2)\times{}\left(\frac{-3}{5}{bxa}^2\right)=\frac{1}{3}\ x^3\ a^3\ b$
5. $\left(\frac{-2}{3}a^6b^5\right)\times{}\left(\frac{-9}{4}a^3b^3\right)=\frac{3}{2}a^9b^8$
6. $\ (\frac{-5}{8}p^2q)\times{}(\frac{16}{25}{pq}^2)=\frac{-2}{5}p^3q^3$

Question 2: Multiply:

i) $\left(2x^2-5x+6\right)\times{}\left(-3x\right)$

$=-6x^3+15x^2-18x$

ii) $\left(3-2y-y^2\right)\times{}\left(-4xy\right)$

$=-12xy+8{xy}^2+{4xy}^3$

iii) $\left({3x}^2y-2xy^2+5xy-6\right)\times{}4xy$

$={12x}^3y^2-{8x}^2y^3+20x^2y^2-24xy$

iv) $\left(7a^3-5ab^2-{2b}^3+3ab+2a-5\right)\times{}\left(-3{ab}^2\right)$

$= b^2+15\ a^2b^4+{6ab}^5-9\ a^2b^3-{6a}^2b^2+{15ab}^2$

Question 3: Multiply:

i) $\left(a+5\right)\left(a+4\right)=a^2+9a+20$

ii) $\left(x-3\right)\left(x+8\right)=x^2-3x+8x-24$

$=x^2+5x-24$

iii) $\left(y-4\right)\left(y-6\right)=y^2-4y-6y+24$

$=y^2+10y+24$

iv) $\left(z+1\right)\left(z-7\right)=\ z^2+z-7z-7$

$=z^2-6z-7$

v) $\left(3a-2b\right)\left(2a+3b\right)={6a}^2-4ab+9ab-{6b}^2$

$={6a}^2+5ab-{6b}^2$

vi) $\left(5x+4y\right)\left(2x-3y\right)={10x}^2+8xy-15xy-12y^2$

$=10x^2-7xy-12y^2$

Question 4: Multiply:

i) $(4x^2+3x-5)\times{}(2x+3)$

$=8x^3+{6x}^2-10x+{12x}^2+9x-15$

$={8x}^3+{18x}^2-x-15$

ii) $(3-2x+5x^2)\times{}(5x-4)$

$=15x-10x^2+25x^3-12+8x-20x^2$

$=25x^3-30x^2+23x-12$

iii) $\left(x^3-5x+3\right)\left(2x+9\right)$

$={2x}^4-{10x}^2+6x+{9x}^3-45x+27$

$=2x^4+{9x}^3-10x^2-39x+27$

iv) $\left(4x^2+xy+{9y}^2\right)\times{}\left(2x-3y\right)$

$={8x}^3+{2x}^2y+18{xy}^2-12x^2y-{6xy}^2-27y^3$

$={8x}^3-27y^3-10x^2y+12{xy}^2$

Question 5: Multiply:

i) $\left({4x}^2-4x+1\right)\times{}({2x}^2+x-2)$

$={8x}^4-{8x}^3+{2x}^2+{4x}^3-{4x}^2+x-{8x}^2+8x-2$

$={8x}^4-{4x}^3-{10x}^2+9x-2$

ii) $\left({3x}^2+4x-5\right)\times{}\left({4x}^2-7x+2\right)$

$=12x^4+{16x}^3-20x^2-{21x}^3-{28x}^2+35x+{6x}^2+8x-10$

$=12x^4-5x^3-42x^2+43x-10$

iii) $\left({4x}^2+24xy+{3y}^2\right)\left(x^2-xy+y^2\right)$

$={4x}^4+{24x}^3y+{3x}^2y^2-{4x}^3y-24x^2y^2-3xy^3 \\ +4x^2y^2+24xy^3+4y^4$

$={4x}^4+{20x}^3y-{17x}^2y^2+{21xy}^3+3y^4$

iv) $\left({6x}^3-{5x}^2+4x+1\right)\times{}\left(x^2+7x-1\right)$

$=6x^5-{5x}^4+{4x}^3+x^2+{42x}^4-35x^3+28x^2+7x-6x^3 \\ +5x^2-4x-1+3x-1$

$=6x^5+37x^4-37x^3+34x^2+3x-1$

v) $\left(8x^4-{3x}^2+9x-8\right)\times{}\left(2x^2-5x+3\right)$

$=16x^6-{6x}^4+{18x}^3-{16x}^2-40x^5 \\ +{15x}^3-45x^2+40x+{24x}^4-{9x}^2+27x-24$

$=16x^6-{40x}^5+18x^4+33x^3-70x^2+67x-24$

vi) $\left(3x^5-{7x}^3+2x^2-x+4\right)\times{}\left(x^3-{2x}^2+3x-1\right)$

$={3x}^8-7x^6+{2x}^5-x^4+{4x}^3+14x^5-4x^4 \\ +{2x}^3-6x^7-8x^2+9x^6-21x^4+{6x}^3-{3x}^2\\ +12x-3x^5 +{7x}^3-{2x}^2+x-4$

$=3x^8+2x^6+13x^5-{26x}^4+{19x}^3-{6x}^7+{13x}^2+13x-4$