# Test: Algebra II - Challenging

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Question 1:   Simplify the expression: $3\frac{2}{3}x\left(6{x}^{2}-9x+\frac{3}{8}\right)$
$19{x}^{3}-28{x}^{2}-2\frac{1}{3}x$
$22{x}^{3}-33{x}^{2}+1\frac{3}{8}x$
$12{x}^{3}-11{x}^{2}+5\frac{3}{8}x$
$18\frac{2}{3}{x}^{3}-27\frac{2}{3}{x}^{2}+3\frac{7}{8}x$$3x-8$
Question 2:   Simplify the expression: $\frac{4{x}^{2}-8}{2}-\frac{16{x}^{2}+24}{4}$
$-2{x}^{2}+12$
$-2{x}^{2}-4$
$-2{x}^{2}-10$
$2{x}^{2}+8$
Question 3:   Simplify the expression: $\frac{2}{3}R\left(6R-18\right)-\frac{1}{5}\left(24+15P\right)$
$-3{R}^{2}+2P-11$
$4R-P+13$
$4{R}^{2}-12R-3P-4\frac{4}{5}$
$\frac{4}{5}{R}^{2}-5P-15\frac{2}{3}$
Question 4:   Simplify the expression by collecting like terms: $2xy+5xz+2x\left(3yz-y\right)-z\left(x-xy\right)+xz\left(5y-4\right)$
$0$
$2xy+2xz$
$xy+6xyz$
$12xyz$
Question 5:   Simplify the expression by collecting like terms: $2x\left(1-y\right)-3\left(x-y\right)+y\left(x+2\right)+xy$
$-x+5y$
$-\frac{1}{2}x+3y$
$x+y$
$-x+2y$
Question 6:   Simplify and factorise the expression: $3xy-2zx-7zy-6xz+yx$
$6y\left(x-2z\right)$
$6x\left(\frac{32}{7}y-\frac{10}{7}z+8\right)$
$3z\left(2x-3y\right)+4xy$
$4x\left(y-2z\right)-7zy$
Question 7:   Simplify the expression: $2\left(x+y\right)\left(x-y\right)-\left(x+1\right)\left(2x-3\right)$
${x}^{2}-2{y}^{2}-1$
$-2{y}^{2}+x+3$
${x}^{2}+{y}^{2}+5$
$-2{x}^{2}+y-4$
Question 8:   Simplify the expression: ${\left(x-5\right)}^{2}+{\left(x-4\right)}^{2}$
$2x-9$
$2{x}^{2}-18x+41$
$4{x}^{2}-18x+81$
$2{x}^{2}-9x+22$
Question 9:   Simplify the expression: ${\left(x-1\right)}^{2}-\left(x+1\right)\left(x-1\right)$
${x}^{2}-1$
$x$
$0$
$-2x+2$
Question 10:   Simplify the expression by collecting like terms: $2\left(p+q\right)-3r\left(p-2q\right)+q+3\left(p-1\right)\left(q+r\right)$
$2p-3r+6qr+3pq$
$2\left(r\left[3q-p\right]+1\right)$
$5pq\left(r-1\right)$
$6r\left(q-p\right)$