Solve 3x^2(3x+4)^2+x^3*2(x-1)

$$3 x ^ { 2 } ( 3 x + 4 ) ^ { 2 } + x ^ { 3 } \cdot 2 ( x - 1 )$$

Evaluate

$$x^{2}\left(29x^{2}+70x+48\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4\right)^{2}.

$$3x^{2}\left(9x^{2}+24x+16\right)+x^{3}\times 2\left(x-1\right)$$

Use the distributive property to multiply 3x^{2} by 9x^{2}+24x+16.

$$27x^{4}+72x^{3}+48x^{2}+x^{3}\times 2\left(x-1\right)$$

Use the distributive property to multiply x^{3}\times 2 by x-1.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-x^{3}\times 2$$

Multiply -1 and 2 to get -2.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-2x^{3}$$

Combine 27x^{4} and 2x^{4} to get 29x^{4}.

$$29x^{4}+72x^{3}+48x^{2}-2x^{3}$$

Combine 72x^{3} and -2x^{3} to get 70x^{3}.

$$29x^{4}+70x^{3}+48x^{2}$$

Expand

$$29x^{4}+70x^{3}+48x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4\right)^{2}.

$$3x^{2}\left(9x^{2}+24x+16\right)+x^{3}\times 2\left(x-1\right)$$

Use the distributive property to multiply 3x^{2} by 9x^{2}+24x+16.

$$27x^{4}+72x^{3}+48x^{2}+x^{3}\times 2\left(x-1\right)$$

Use the distributive property to multiply x^{3}\times 2 by x-1.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-x^{3}\times 2$$

Multiply -1 and 2 to get -2.

$$27x^{4}+72x^{3}+48x^{2}+2x^{4}-2x^{3}$$

Combine 27x^{4} and 2x^{4} to get 29x^{4}.

$$29x^{4}+72x^{3}+48x^{2}-2x^{3}$$

Combine 72x^{3} and -2x^{3} to get 70x^{3}.

$$29x^{4}+70x^{3}+48x^{2}$$