Solve (3x-9)(-5x-3)+(3x-0)(8x+9)

$$( 3 x - 9 ) ( - 5 x - 3 ) + ( 3 x - 0 ) ( 8 x + 9 )$$

Evaluate

$$9\left(x^{2}+7x+3\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 3x-9 by each term of -5x-3.

$$-15x^{2}-9x+45x+27+\left(3x-0\right)\left(8x+9\right)$$

Combine -9x and 45x to get 36x.

$$-15x^{2}+36x+27+\left(3x-0\right)\left(8x+9\right)$$

Use the distributive property to multiply 3x-0 by 8x+9.

$$-15x^{2}+36x+27+8\left(3x-0\right)x+9\left(3x-0\right)$$

Multiply -1 and 0 to get 0.

$$-15x^{2}+36x+27+8\left(3x+0\right)x+9\left(3x-0\right)$$

Anything plus zero gives itself.

$$-15x^{2}+36x+27+8\times 3xx+9\left(3x-0\right)$$

Multiply 8 and 3 to get 24.

$$-15x^{2}+36x+27+24xx+9\left(3x-0\right)$$

Multiply x and x to get x^{2}.

$$-15x^{2}+36x+27+24x^{2}+9\left(3x-0\right)$$

Combine -15x^{2} and 24x^{2} to get 9x^{2}.

$$9x^{2}+36x+27+9\left(3x-0\right)$$

Multiply -1 and 0 to get 0.

$$9x^{2}+36x+27+9\left(3x+0\right)$$

Anything plus zero gives itself.

$$9x^{2}+36x+27+9\times 3x$$

Multiply 9 and 3 to get 27.

$$9x^{2}+36x+27+27x$$

Combine 36x and 27x to get 63x.

$$9x^{2}+63x+27$$

Expand

$$9x^{2}+63x+27$$

Solution Steps

Apply the distributive property by multiplying each term of 3x-9 by each term of -5x-3.

$$-15x^{2}-9x+45x+27+\left(3x-0\right)\left(8x+9\right)$$

Combine -9x and 45x to get 36x.

$$-15x^{2}+36x+27+\left(3x-0\right)\left(8x+9\right)$$

Use the distributive property to multiply 3x-0 by 8x+9.

$$-15x^{2}+36x+27+8\left(3x-0\right)x+9\left(3x-0\right)$$

Multiply -1 and 0 to get 0.

$$-15x^{2}+36x+27+8\left(3x+0\right)x+9\left(3x-0\right)$$

Anything plus zero gives itself.

$$-15x^{2}+36x+27+8\times 3xx+9\left(3x-0\right)$$

Multiply 8 and 3 to get 24.

$$-15x^{2}+36x+27+24xx+9\left(3x-0\right)$$

Multiply x and x to get x^{2}.

$$-15x^{2}+36x+27+24x^{2}+9\left(3x-0\right)$$

Combine -15x^{2} and 24x^{2} to get 9x^{2}.

$$9x^{2}+36x+27+9\left(3x-0\right)$$

Multiply -1 and 0 to get 0.

$$9x^{2}+36x+27+9\left(3x+0\right)$$

Anything plus zero gives itself.

$$9x^{2}+36x+27+9\times 3x$$

Multiply 9 and 3 to get 27.

$$9x^{2}+36x+27+27x$$

Combine 36x and 27x to get 63x.

$$9x^{2}+63x+27$$