Solve 9/4^2a-B^2+25B^2

$$9 / 4 ^ { 2 } a - B ^ { 2 } + 25 B ^ { 2 }$$

Evaluate

$$24B^{2}+\frac{81a}{16}$$

Solution Steps

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$\frac{81}{16}a-B^{2}+25B^{2}$$

Combine -B^{2} and 25B^{2} to get 24B^{2}.

$$\frac{81}{16}a+24B^{2}$$

Factor

$$\frac{3\left(128B^{2}+27a\right)}{16}$$

Solution Steps

Factor out \frac{1}{16}.

$$\frac{81a-16B^{2}+400B^{2}}{16}$$

Consider 81a-16B^{2}+400B^{2}. Multiply and combine like terms.

$$384B^{2}+81a$$

Consider 384B^{2}+81a. Factor out 3.

$$3\left(128B^{2}+27a\right)$$

Rewrite the complete factored expression.

$$\frac{3\left(128B^{2}+27a\right)}{16}$$