Solve =(3x-4)(x-3)+(x-1)(x+1)+(8x+1)

$$= ( 3 x - 4 ) ( x - 3 ) + ( x - 1 ) ( x + 1 ) + ( 8 x + 1 )$$

Evaluate

$$4x^{2}-5x+12$$

Solution Steps

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

$$3x^{2}-9x-4x+12+\left(x-1\right)\left(x+1\right)+8x+1$$

Combine -9x and -4x to get -13x.

$$3x^{2}-13x+12+\left(x-1\right)\left(x+1\right)+8x+1$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3x^{2}-13x+12+x^{2}-1^{2}+8x+1$$

Calculate 1 to the power of 2 and get 1.

$$3x^{2}-13x+12+x^{2}-1+8x+1$$

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

$$4x^{2}-13x+12-1+8x+1$$

Subtract 1 from 12 to get 11.

$$4x^{2}-13x+11+8x+1$$

Combine -13x and 8x to get -5x.

$$4x^{2}-5x+11+1$$

Add 11 and 1 to get 12.

$$4x^{2}-5x+12$$

Expand

$$4x^{2}-5x+12$$

Solution Steps

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

$$3x^{2}-9x-4x+12+\left(x-1\right)\left(x+1\right)+8x+1$$

Combine -9x and -4x to get -13x.

$$3x^{2}-13x+12+\left(x-1\right)\left(x+1\right)+8x+1$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3x^{2}-13x+12+x^{2}-1^{2}+8x+1$$

Calculate 1 to the power of 2 and get 1.

$$3x^{2}-13x+12+x^{2}-1+8x+1$$

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

$$4x^{2}-13x+12-1+8x+1$$

Subtract 1 from 12 to get 11.

$$4x^{2}-13x+11+8x+1$$

Combine -13x and 8x to get -5x.

$$4x^{2}-5x+11+1$$

Add 11 and 1 to get 12.

$$4x^{2}-5x+12$$