Solve (3x+2)(3x-2)-5x(x-1)-(2x-1)^2

$$( 3 x + 2 ) ( 3 x - 2 ) - 5 x ( x - 1 ) - ( 2 x - 1 ) ^ { 2 }$$

Evaluate

$$9x-5$$

Solution Steps

Consider \left(3x+2\right)\left(3x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$\left(3x\right)^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}$$

Expand \left(3x\right)^{2}.

$$3^{2}x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

$$9x^{2}-4-5x\left(x-1\right)-\left(4x^{2}-4x+1\right)$$

To find the opposite of 4x^{2}-4x+1, find the opposite of each term.

$$9x^{2}-4-5x\left(x-1\right)-4x^{2}+4x-1$$

Use the distributive property to multiply -5x by x-1.

$$9x^{2}-4-5x^{2}+5x-4x^{2}+4x-1$$

Combine 9x^{2} and -5x^{2} to get 4x^{2}.

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

Combine 4x^{2} and -4x^{2} to get 0.

$$-4+5x+4x-1$$

Combine 5x and 4x to get 9x.

$$-4+9x-1$$

Subtract 1 from -4 to get -5.

$$-5+9x$$

Expand

$$9x-5$$

Solution Steps

Consider \left(3x+2\right)\left(3x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$\left(3x\right)^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}$$

Expand \left(3x\right)^{2}.

$$3^{2}x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

$$9x^{2}-4-5x\left(x-1\right)-\left(4x^{2}-4x+1\right)$$

To find the opposite of 4x^{2}-4x+1, find the opposite of each term.

$$9x^{2}-4-5x\left(x-1\right)-4x^{2}+4x-1$$

Use the distributive property to multiply -5x by x-1.

$$9x^{2}-4-5x^{2}+5x-4x^{2}+4x-1$$

Combine 9x^{2} and -5x^{2} to get 4x^{2}.

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

Combine 4x^{2} and -4x^{2} to get 0.

$$-4+5x+4x-1$$

Combine 5x and 4x to get 9x.

$$-4+9x-1$$

Subtract 1 from -4 to get -5.

$$-5+9x$$