Solve -(25-3/4a)^2+(25+9/4)^2

$$- ( 25 - \frac { 3 } { 4 } a ) ^ { 2 } + ( 25 + \frac { 9 } { 4 } ) ^ { 2 }$$

Evaluate

$$-\frac{9a^{2}}{16}+\frac{75a}{2}+\frac{1881}{16}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(25-\frac{3}{4}a\right)^{2}.

$$-\left(625-\frac{75}{2}a+\frac{9}{16}a^{2}\right)+\left(25+\frac{9}{4}\right)^{2}$$

To find the opposite of 625-\frac{75}{2}a+\frac{9}{16}a^{2}, find the opposite of each term.

$$-625+\frac{75}{2}a-\frac{9}{16}a^{2}+\left(25+\frac{9}{4}\right)^{2}$$

Add 25 and \frac{9}{4} to get \frac{109}{4}.

$$-625+\frac{75}{2}a-\frac{9}{16}a^{2}+\left(\frac{109}{4}\right)^{2}$$

Calculate \frac{109}{4} to the power of 2 and get \frac{11881}{16}.

$$-625+\frac{75}{2}a-\frac{9}{16}a^{2}+\frac{11881}{16}$$

Add -625 and \frac{11881}{16} to get \frac{1881}{16}.

$$\frac{1881}{16}+\frac{75}{2}a-\frac{9}{16}a^{2}$$

Expand

$$-\frac{9a^{2}}{16}+\frac{75a}{2}+\frac{1881}{16}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(25-\frac{3}{4}a\right)^{2}.

$$-\left(625-\frac{75}{2}a+\frac{9}{16}a^{2}\right)+\left(25+\frac{9}{4}\right)^{2}$$

To find the opposite of 625-\frac{75}{2}a+\frac{9}{16}a^{2}, find the opposite of each term.

$$-625+\frac{75}{2}a-\frac{9}{16}a^{2}+\left(25+\frac{9}{4}\right)^{2}$$

Add 25 and \frac{9}{4} to get \frac{109}{4}.

$$-625+\frac{75}{2}a-\frac{9}{16}a^{2}+\left(\frac{109}{4}\right)^{2}$$

Calculate \frac{109}{4} to the power of 2 and get \frac{11881}{16}.

$$-625+\frac{75}{2}a-\frac{9}{16}a^{2}+\frac{11881}{16}$$

Add -625 and \frac{11881}{16} to get \frac{1881}{16}.

$$\frac{1881}{16}+\frac{75}{2}a-\frac{9}{16}a^{2}$$