Solve 5*(15^2+18^2)-3*18*(15+18)-5*15*(15-3*18)/48^2+2*48*15-8*15^2

$$\frac { 5 \times ( 15 ^ { 2 } + 18 ^ { 2 } ) - 3 \times 18 \times ( 15 + 18 ) - 5 \times 15 \times ( 15 - 3 \times 18 ) } { 48 ^ { 2 } + 2 \times 48 \times 15 - 8 \times 15 ^ { 2 } }$$

Evaluate

$$2$$

Solution Steps

Calculate 15 to the power of 2 and get 225.

$$\frac{5\left(225+18^{2}\right)-3\times 18\left(15+18\right)-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Calculate 18 to the power of 2 and get 324.

$$\frac{5\left(225+324\right)-3\times 18\left(15+18\right)-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Add 225 and 324 to get 549.

$$\frac{5\times 549-3\times 18\left(15+18\right)-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Multiply 5 and 549 to get 2745.

$$\frac{2745-3\times 18\left(15+18\right)-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Multiply 3 and 18 to get 54.

$$\frac{2745-54\left(15+18\right)-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Add 15 and 18 to get 33.

$$\frac{2745-54\times 33-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Multiply 54 and 33 to get 1782.

$$\frac{2745-1782-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Subtract 1782 from 2745 to get 963.

$$\frac{963-5\times 15\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Multiply 5 and 15 to get 75.

$$\frac{963-75\left(15-3\times 18\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Multiply 3 and 18 to get 54.

$$\frac{963-75\left(15-54\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Subtract 54 from 15 to get -39.

$$\frac{963-75\left(-39\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Multiply 75 and -39 to get -2925.

$$\frac{963-\left(-2925\right)}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

The opposite of -2925 is 2925.

$$\frac{963+2925}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Add 963 and 2925 to get 3888.

$$\frac{3888}{48^{2}+2\times 48\times 15-8\times 15^{2}}$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{3888}{2304+2\times 48\times 15-8\times 15^{2}}$$

Multiply 2 and 48 to get 96.

$$\frac{3888}{2304+96\times 15-8\times 15^{2}}$$

Multiply 96 and 15 to get 1440.

$$\frac{3888}{2304+1440-8\times 15^{2}}$$

Add 2304 and 1440 to get 3744.

$$\frac{3888}{3744-8\times 15^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{3888}{3744-8\times 225}$$

Multiply 8 and 225 to get 1800.

$$\frac{3888}{3744-1800}$$

Subtract 1800 from 3744 to get 1944.

$$\frac{3888}{1944}$$

Divide 3888 by 1944 to get 2.

$$2$$

Factor

$$2$$