Solve (3x^2+1)(15x^2+8x)+(5x^3+4x^2-1)(6x)

$$( 3 x ^ { 2 } + 1 ) ( 15 x ^ { 2 } + 8 x ) + ( 5 x ^ { 3 } + 4 x ^ { 2 } - 1 ) ( 6 x )$$

Evaluate

$$x\left(75x^{3}+48x^{2}+15x+2\right)$$

Solution Steps

Use the distributive property to multiply 3x^{2}+1 by 15x^{2}+8x.

$$45x^{4}+24x^{3}+15x^{2}+8x+\left(5x^{3}+4x^{2}-1\right)\times 6x$$

Use the distributive property to multiply 5x^{3}+4x^{2}-1 by 6.

$$45x^{4}+24x^{3}+15x^{2}+8x+\left(30x^{3}+24x^{2}-6\right)x$$

Use the distributive property to multiply 30x^{3}+24x^{2}-6 by x.

$$45x^{4}+24x^{3}+15x^{2}+8x+30x^{4}+24x^{3}-6x$$

Combine 45x^{4} and 30x^{4} to get 75x^{4}.

$$75x^{4}+24x^{3}+15x^{2}+8x+24x^{3}-6x$$

Combine 24x^{3} and 24x^{3} to get 48x^{3}.

$$75x^{4}+48x^{3}+15x^{2}+8x-6x$$

Combine 8x and -6x to get 2x.

$$75x^{4}+48x^{3}+15x^{2}+2x$$

Expand

$$75x^{4}+48x^{3}+15x^{2}+2x$$

Solution Steps

Use the distributive property to multiply 3x^{2}+1 by 15x^{2}+8x.

$$45x^{4}+24x^{3}+15x^{2}+8x+\left(5x^{3}+4x^{2}-1\right)\times 6x$$

Use the distributive property to multiply 5x^{3}+4x^{2}-1 by 6.

$$45x^{4}+24x^{3}+15x^{2}+8x+\left(30x^{3}+24x^{2}-6\right)x$$

Use the distributive property to multiply 30x^{3}+24x^{2}-6 by x.

$$45x^{4}+24x^{3}+15x^{2}+8x+30x^{4}+24x^{3}-6x$$

Combine 45x^{4} and 30x^{4} to get 75x^{4}.

$$75x^{4}+24x^{3}+15x^{2}+8x+24x^{3}-6x$$

Combine 24x^{3} and 24x^{3} to get 48x^{3}.

$$75x^{4}+48x^{3}+15x^{2}+8x-6x$$

Combine 8x and -6x to get 2x.

$$75x^{4}+48x^{3}+15x^{2}+2x$$