# Test: Algebraic expressions I - Normal

Double click on maths expressions to zoom
Question 1:   Expand and simplify: $\left(x-2\right)\left(x+3\right)=...$
${x}^{2}+x-6$
${x}^{2}+5x-6$
${x}^{2}+2x-6$
${x}^{2}+x+6$
Question 2:   Expand and simplify: $\left(x-1\right)\left(x-1\right)=...$
${x}^{2}-4x+1$
${x}^{2}-2x+1$
${x}^{2}-x+1$
${x}^{2}-1$
Question 3:   Simplify $\frac{3{x}^{2}{x}^{5}}{\left(y-1\right){x}^{3}}=...$
$\frac{3{x}^{4}}{\left(y-1\right){x}^{3}}$
$\frac{3{x}^{7}}{y-1}$
$\frac{3{x}^{4}}{y-1}$
$\frac{3{x}^{7}}{\left(y-1\right){x}^{3}}$
Question 4:   Simplify: ${\left(12{x}^{5}{y}^{3}\right)}^{0}=...$  for $\text{\hspace{0.17em}}x\ne 0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}y\ne 0\text{\hspace{0.17em}}$.
$12{x}^{5}{y}^{3}$
$0$
$1$
$144{x}^{10}{y}^{6}$
Question 5:   Simplify: ${\left(\frac{2{x}^{3}{y}^{2}}{{x}^{2}}\right)}^{2}=...$
$4{x}^{2}{y}^{4}$
$4{x}^{6}{y}^{4}$
$4{x}^{8}{y}^{4}$
$2{x}^{4}{y}^{6}$
Question 6:   Simplify: $\left(x-3\right){\left(x-3\right)}^{-2}=...$
$\frac{1}{{x}^{2}-9}$
$\frac{1}{x-3}$
$\frac{1}{{\left(x-3\right)}^{2}}$
${x}^{2}-6x+9$
Question 7:   Simplify: $\frac{{x}^{2}-2x-8}{{x}^{2}+4x+4}=...$
$\frac{1}{x+2}$
$\frac{x-4}{x+2}$
$\frac{x+2}{x-2}$
$1$
Question 8:   Simplify: ${x}^{3}\left(x-2\right)÷{\left(x-2\right)}^{2}=...$
$\frac{{x}^{3}}{x-2}$
${x}^{3}\left(x-2\right)$
$\frac{{x}^{3}}{{\left(x-2\right)}^{3}}$
$\frac{{x}^{3}}{{\left(x-2\right)}^{2}}$
Question 9:   Simplify: $\frac{{x}^{2}-16x+64}{x-8}=...$
$1$
$\frac{1}{{\left(x-8\right)}^{2}}$
$x-8$
$\frac{1}{x-8}$
Question 10:   Factorise: $8{x}^{3}-1=...$
$\left(2x-1\right)\left(4{x}^{2}+2x+1\right)$
$\left(2x-1\right)\left(4{x}^{2}-2x+1\right)$
$\left(2x-1\right)\left(4{x}^{2}-4x+1\right)$
$\left(2x-1\right)\left(4{x}^{2}+4x+1\right)$