Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$a4-2a3+ \frac{ 3 }{ 2 } { a }^{ 2 } - \frac{ 1 }{ 2 } a+ \frac{ 1 }{ 16 }$$

Answer

$$-(5*a)/2+(3*a^2)/2+1/16$$

Solution


Regroup terms.
\[4a-2a\times 3+\frac{3}{2}{a}^{2}-\frac{1}{2}a+\frac{1}{16}\]
Simplify  \(2a\times 3\)  to  \(6a\).
\[4a-6a+\frac{3}{2}{a}^{2}-\frac{1}{2}a+\frac{1}{16}\]
Simplify  \(\frac{3}{2}{a}^{2}\)  to  \(\frac{3{a}^{2}}{2}\).
\[4a-6a+\frac{3{a}^{2}}{2}-\frac{1}{2}a+\frac{1}{16}\]
Simplify  \(\frac{1}{2}a\)  to  \(\frac{a}{2}\).
\[4a-6a+\frac{3{a}^{2}}{2}-\frac{a}{2}+\frac{1}{16}\]
Collect like terms.
\[(4a-6a-\frac{a}{2})+\frac{3{a}^{2}}{2}+\frac{1}{16}\]
Simplify.
\[-\frac{5a}{2}+\frac{3{a}^{2}}{2}+\frac{1}{16}\]
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