# Test: Algebraic expressions I - Ambitious

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Question 1:   Expand and simplify: $4x{y}^{3}\left(xy-5{y}^{2}\right)=...$
$4{x}^{2}{y}^{4}-20x{y}^{5}$
$4{x}^{2}{y}^{4}-20x{y}^{4}$
$4{x}^{2}{y}^{2}-20x{y}^{5}$
$4{x}^{2}{y}^{4}-5x{y}^{5}$
Question 2:   Expand and simplify: $\left({x}^{2}-6\right)\left(2x-7\right)=...$
$2{x}^{3}-7{x}^{2}+42$
$2{x}^{3}-7x-12x+42$
$2{x}^{3}-19{x}^{2}+42$
$2{x}^{3}-7{x}^{2}-12x+42$
Question 3:   Simplify: $\frac{9{x}^{2}-{y}^{2}}{3x+y}\left(3x-y\right)=...$
$3x+y$
$3x-y$
$1$
$9{x}^{2}-6xy+{y}^{2}$
Question 4:   Find remainder of division ${x}^{3}-4{x}^{2}+x+7$ by $x-1$
$0$
$4$
$1$
$5$
Question 5:   Find remainder of division ${x}^{3}+6{x}^{2}+x-4$ by $x+1$
$2$
$1$
$0$
$5$
Question 6:   Factorise: $-6{x}^{3}+{x}^{2}+6x-1$
$\left(6x-1\right)\left(1-x\right)\left(1+x\right)$
$\left(6x-1\right)\left(6x+1\right)\left(1-x\right)$
$\left(6x-1\right){\left(1-x\right)}^{2}$
$\left(6x-1\right)\left(1-{x}^{2}\right)$
Question 7:   Factorise ${x}^{4}-2{x}^{2}+1$
${\left(x-1\right)}^{2}$
${\left({x}^{2}-1\right)}^{2}$
$\left(x-1\right)\left(x+1\right)$
${\left(x-1\right)}^{2}{\left(x+1\right)}^{2}$
Question 8:   Simplify: $\frac{\left(x-4\right)\left({x}^{2}-5x+4\right)}{{x}^{2}-8x+16}$
$\frac{x-1}{x-4}$
$1$
$x-4$
$x-1$
Question 9:   Simplify: $\frac{16\left({x}^{3}-1\right)}{12\left({x}^{2}+x+1\right)}$ 
$\frac{16}{12}\left(x-1\right)$
$\frac{4}{3}\left({x}^{2}+x+1\right)$
$\frac{4}{3}\left({x}^{3}-1\right)$
$\frac{4}{3}\left(x-1\right)$
Question 10:   Simplify: ${\left(x-y\right)}^{\frac{2}{3}}÷{\left(x-y\right)}^{\frac{1}{6}}$
$1$
${\left(x-y\right)}^{\frac{1}{2}}$
${\left(x-y\right)}^{2}$
${\left(x-y\right)}^{\frac{1}{6}}$