What is expand ((6-y)/2)^2 ?

The solution to expand ((6-y)/2)^2 is (y^2)/4-3y+9

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expand ((6-y)/2)^2

expand

(\frac{6 - y}{2})^{2}

\frac{y ^{2}}{4} - 3 y + 9

Solution steps

(\frac{6 - y}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 6 - y ) ^{2}}{2 ^{2}}

(6 - y)^{2} = 36 - 12 y + y^{2}

= \frac{36 - 12 y + y ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{36 - 12 y + y ^{2}}{4}

Apply the fraction rule:

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

\frac{36 - 12 y + y ^{2}}{4} = \frac{36}{4} - \frac{12 y}{4} + \frac{y ^{2}}{4}

= \frac{36}{4} - \frac{12 y}{4} + \frac{y ^{2}}{4}

Divide the numbers:

\frac{36}{4} = 9

= 9 - \frac{12 y}{4} + \frac{y ^{2}}{4}

Divide the numbers:

\frac{12}{4} = 3

= 9 - 3 y + \frac{y ^{2}}{4}

Rewrite in standard form

= \frac{y ^{2}}{4} - 3 y + 9

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