Solve (2+s)^2-{(-2)^2-[(3)(4)-(8+2)]}

$$( 2 + s ) ^ { 2 } - \{ ( - 2 ) ^ { 2 } - [ ( 3 ) ( 4 ) - ( 8 + 2 ) ] \}$$

Evaluate

$$\left(s+2\right)^{2}-2$$

Solution Steps

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

$$4+4s+s^{2}-\left(\left(-2\right)^{2}-\left(3\times 4-\left(8+2\right)\right)\right)$$

Calculate -2 to the power of 2 and get 4.

$$4+4s+s^{2}-\left(4-\left(3\times 4-\left(8+2\right)\right)\right)$$

Multiply 3 and 4 to get 12.

$$4+4s+s^{2}-\left(4-\left(12-\left(8+2\right)\right)\right)$$

Add 8 and 2 to get 10.

$$4+4s+s^{2}-\left(4-\left(12-10\right)\right)$$

Subtract 10 from 12 to get 2.

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

Subtract 2 from 4 to get 2.

$$4+4s+s^{2}-2$$

Subtract 2 from 4 to get 2.

$$2+4s+s^{2}$$

Expand

$$s^{2}+4s+2$$

Solution Steps

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

$$4+4s+s^{2}-\left(\left(-2\right)^{2}-\left(3\times 4-\left(8+2\right)\right)\right)$$

Calculate -2 to the power of 2 and get 4.

$$4+4s+s^{2}-\left(4-\left(3\times 4-\left(8+2\right)\right)\right)$$

Multiply 3 and 4 to get 12.

$$4+4s+s^{2}-\left(4-\left(12-\left(8+2\right)\right)\right)$$

Add 8 and 2 to get 10.

$$4+4s+s^{2}-\left(4-\left(12-10\right)\right)$$

Subtract 10 from 12 to get 2.

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

Subtract 2 from 4 to get 2.

$$4+4s+s^{2}-2$$

Subtract 2 from 4 to get 2.

$$2+4s+s^{2}$$