Solve (4x-1)*(4x+1)-(4x+17)+(4-1)^2+2*4

$$( 4 x - 1 ) \cdot ( 4 x + 1 ) - ( 4 x + 17 ) + ( 4 - 1 ) ^ { 2 } + 2 \cdot 4$$

Evaluate

$$16x^{2}-4x-1$$

Solution Steps

Consider \left(4x-1\right)\left(4x+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}. Square 1.

$$\left(4x\right)^{2}-1-\left(4x+17\right)+\left(4-1\right)^{2}+2\times 4$$

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}-1-\left(4x+17\right)+\left(4-1\right)^{2}+2\times 4$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}-1-\left(4x+17\right)+\left(4-1\right)^{2}+2\times 4$$

To find the opposite of 4x+17, find the opposite of each term.

$$16x^{2}-1-4x-17+\left(4-1\right)^{2}+2\times 4$$

Subtract 17 from -1 to get -18.

$$16x^{2}-18-4x+\left(4-1\right)^{2}+2\times 4$$

Subtract 1 from 4 to get 3.

$$16x^{2}-18-4x+3^{2}+2\times 4$$

Calculate 3 to the power of 2 and get 9.

$$16x^{2}-18-4x+9+2\times 4$$

Add -18 and 9 to get -9.

$$16x^{2}-9-4x+2\times 4$$

Multiply 2 and 4 to get 8.

$$16x^{2}-9-4x+8$$

Add -9 and 8 to get -1.

$$16x^{2}-1-4x$$

Expand

$$16x^{2}-4x-1$$

Solution Steps

Consider \left(4x-1\right)\left(4x+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}. Square 1.

$$\left(4x\right)^{2}-1-\left(4x+17\right)+\left(4-1\right)^{2}+2\times 4$$

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}-1-\left(4x+17\right)+\left(4-1\right)^{2}+2\times 4$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}-1-\left(4x+17\right)+\left(4-1\right)^{2}+2\times 4$$

To find the opposite of 4x+17, find the opposite of each term.

$$16x^{2}-1-4x-17+\left(4-1\right)^{2}+2\times 4$$

Subtract 17 from -1 to get -18.

$$16x^{2}-18-4x+\left(4-1\right)^{2}+2\times 4$$

Subtract 1 from 4 to get 3.

$$16x^{2}-18-4x+3^{2}+2\times 4$$

Calculate 3 to the power of 2 and get 9.

$$16x^{2}-18-4x+9+2\times 4$$

Add -18 and 9 to get -9.

$$16x^{2}-9-4x+2\times 4$$

Multiply 2 and 4 to get 8.

$$16x^{2}-9-4x+8$$

Add -9 and 8 to get -1.

$$16x^{2}-1-4x$$