Solve (x+3)(4x-1)-(x+3)(x-9)

$$( x + 3 ) ( 4 x - 1 ) - ( x + 3 ) ( x - 9 )$$

Evaluate

$$\left(x+3\right)\left(3x+8\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of 4x-1.

$$4x^{2}-x+12x-3-\left(x+3\right)\left(x-9\right)$$

Combine -x and 12x to get 11x.

$$4x^{2}+11x-3-\left(x+3\right)\left(x-9\right)$$

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

$$4x^{2}+11x-3-\left(x^{2}-9x+3x-27\right)$$

Combine -9x and 3x to get -6x.

$$4x^{2}+11x-3-\left(x^{2}-6x-27\right)$$

To find the opposite of x^{2}-6x-27, find the opposite of each term.

$$4x^{2}+11x-3-x^{2}-\left(-6x\right)-\left(-27\right)$$

The opposite of -6x is 6x.

$$4x^{2}+11x-3-x^{2}+6x-\left(-27\right)$$

The opposite of -27 is 27.

$$4x^{2}+11x-3-x^{2}+6x+27$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+11x-3+6x+27$$

Combine 11x and 6x to get 17x.

$$3x^{2}+17x-3+27$$

Add -3 and 27 to get 24.

$$3x^{2}+17x+24$$

Expand

$$3x^{2}+17x+24$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of 4x-1.

$$4x^{2}-x+12x-3-\left(x+3\right)\left(x-9\right)$$

Combine -x and 12x to get 11x.

$$4x^{2}+11x-3-\left(x+3\right)\left(x-9\right)$$

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

$$4x^{2}+11x-3-\left(x^{2}-9x+3x-27\right)$$

Combine -9x and 3x to get -6x.

$$4x^{2}+11x-3-\left(x^{2}-6x-27\right)$$

To find the opposite of x^{2}-6x-27, find the opposite of each term.

$$4x^{2}+11x-3-x^{2}-\left(-6x\right)-\left(-27\right)$$

The opposite of -6x is 6x.

$$4x^{2}+11x-3-x^{2}+6x-\left(-27\right)$$

The opposite of -27 is 27.

$$4x^{2}+11x-3-x^{2}+6x+27$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+11x-3+6x+27$$

Combine 11x and 6x to get 17x.

$$3x^{2}+17x-3+27$$

Add -3 and 27 to get 24.

$$3x^{2}+17x+24$$