What is expand ((3a+b)/4)^2-((b^2+ba+a^2)/2) ?

The solution to expand ((3a+b)/4)^2-((b^2+ba+a^2)/2) is (a^2}{16}-(ab)/8-\frac{7b^2)/(16)

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expand ((3a+b)/4)^2-((b^2+ba+a^2)/2)

expand

(\frac{3 a + b}{4})^{2} - (\frac{b ^{2} + ba + a ^{2}}{2})

\frac{a ^{2}}{16} - \frac{ab}{8} - \frac{7 b ^{2}}{16}

Solution steps

(\frac{3 a + b}{4})^{2} - (\frac{b ^{2} + ba + a ^{2}}{2})

Remove parentheses:

(a) = a

= (\frac{3 a + b}{4})^{2} - \frac{b ^{2} + ba + a ^{2}}{2}

(\frac{3 a + b}{4})^{2} = \frac{9 a ^{2} + 6 ab + b ^{2}}{4 ^{2}}

= \frac{9 a ^{2} + 6 ab + b ^{2}}{4 ^{2}} - \frac{a ^{2} + ab + b ^{2}}{2}

4^{2} = 16

= \frac{9 a ^{2} + 6 ab + b ^{2}}{16} - \frac{b ^{2} + ba + a ^{2}}{2}

Least Common Multiplier of

16, 2 : 16

Adjust Fractions based on the LCM

= \frac{9 a ^{2} + 6 ab + b ^{2}}{16} - \frac{( b ^{2} + ba + a ^{2} ) \cdot 8}{16}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{9 a ^{2} + 6 ab + b ^{2} - ( b ^{2} + ba + a ^{2} ) \cdot 8}{16}

Expand

9 a^{2} + 6 ab + b^{2} - (b^{2} + ba + a^{2}) \cdot 8 : a^{2} - 2 ab - 7 b^{2}

= \frac{a ^{2} - 2 ab - 7 b ^{2}}{16}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{a ^{2} - 2 ab - 7 b ^{2}}{16} = \frac{a ^{2}}{16} - \frac{2 ab}{16} - \frac{7 b ^{2}}{16}

= \frac{a ^{2}}{16} - \frac{2 ab}{16} - \frac{7 b ^{2}}{16}

Cancel

\frac{2 ab}{16} : \frac{ab}{8}

= \frac{a ^{2}}{16} - \frac{ab}{8} - \frac{7 b ^{2}}{16}

l im x \Rightarrow 5 (x^{2} - x - 20 x^{2} - 7 x + 10)

\frac{( x + h ) y ^{3} - ( x + h ) ^{3} y}{h}

8 (6 - 4)

\frac{( x + 4 ) ^{4}}{4}

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What is expand ((3a+b)/4)^2-((b^2+ba+a^2)/2) ?
The solution to expand ((3a+b)/4)^2-((b^2+ba+a^2)/2) is (a^2}{16}-(ab)/8-\frac{7b^2)/(16)