# Test: Algebra I - Ambitious

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Question 1:   Simplify: $3{l}^{2}mn+n{l}^{2}m-5m{n}^{2}l+{l}^{2}nm+2{n}^{2}ml-m{n}^{2}$
$mn\left(5{l}^{2}-3nl+m\right)$
${l}^{2}\left(5mn-2ml+n\right)$
$mn\left(5{l}^{2}-3nl-n\right)$
$5mn\left({l}^{2}+nl-m\right)$
Question 2:   Simplify: ${z}^{7}÷{z}^{-x}\cdot {z}^{-{y}^{2}}$
${z}^{7+x-{y}^{2}}$
${z}^{7+x+{y}^{2}}$
$z\left(7-x-{y}^{2}\right)$
${z}^{7-x+{y}^{2}}$
Question 3:   Remove the brackets: $-\left\{-2\left[x-3\left(y-4\right)\right]-5\left(z+6\right)\right\}$
$-2x+3y-5z+20$
$2x-6y-5z-28$
$2x-6y+5z+54$
$2x-6y+5z+6$
Question 4:   Remove logs: $\mathrm{log}F=\mathrm{log}G+\mathrm{log}H-\mathrm{log}\left(\frac{1}{M}\right)-2\mathrm{log}R$
$F=\frac{GHM}{{R}^{2}}$
$F=\frac{GH}{M{R}^{2}}$
$F=G+M-\frac{1}{M}-2R$
$F=2\frac{GH}{MR}$
Question 5:   Rewrite in the logarithmic form: $T=2\pi \sqrt{\frac{L}{G}}$
$\mathrm{log}T=\mathrm{log}\frac{2\pi L}{G}$
$\mathrm{log}T=\mathrm{log}2+\mathrm{log}\pi +\frac{1}{2}\left(\mathrm{log}L-\mathrm{log}G\right)$
$\mathrm{log}T=\mathrm{log}2+\mathrm{log}\pi -{\left(\mathrm{log}L-\mathrm{log}G\right)}^{2}$
$\mathrm{log}T=\mathrm{log}2+\mathrm{log}\pi -\frac{1}{2}\mathrm{log}L-\mathrm{log}G$
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