Solve 4(x-1)(x+1)+(2x-1)(2x+1)

$$4 ( x - 1 ) ( x + 1 ) + ( 2 x - 1 ) ( 2 x + 1 )$$

Evaluate

$$8x^{2}-5$$

Solution Steps

Use the distributive property to multiply 4 by x-1.

$$\left(4x-4\right)\left(x+1\right)+\left(2x-1\right)\left(2x+1\right)$$

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

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

Combine 4x and -4x to get 0.

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

Consider \left(2x-1\right)\left(2x+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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 1 to the power of 2 and get 1.

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

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$8x^{2}-4-1$$

Subtract 1 from -4 to get -5.

$$8x^{2}-5$$

Expand

$$8x^{2}-5$$

Solution Steps

Use the distributive property to multiply 4 by x-1.

$$\left(4x-4\right)\left(x+1\right)+\left(2x-1\right)\left(2x+1\right)$$

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

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

Combine 4x and -4x to get 0.

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

Consider \left(2x-1\right)\left(2x+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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 1 to the power of 2 and get 1.

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

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$8x^{2}-4-1$$

Subtract 1 from -4 to get -5.

$$8x^{2}-5$$