Solve 4(-5+7)^2-(-12+9)^2-[-(-4)*(-5+4)]^2

$$4 ( - 5 + 7 ) ^ { 2 } - ( - 12 + 9 ) ^ { 2 } - [ - ( - 4 ) \cdot ( - 5 + 4 ) ] ^ { 2 }$$

Evaluate

$$-9$$

Solution Steps

Add -5 and 7 to get 2.

$$4\times 2^{2}-\left(-12+9\right)^{2}-\left(\left(-\left(-4\right)\right)\left(-5+4\right)\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\times 4-\left(-12+9\right)^{2}-\left(\left(-\left(-4\right)\right)\left(-5+4\right)\right)^{2}$$

Multiply 4 and 4 to get 16.

$$16-\left(-12+9\right)^{2}-\left(\left(-\left(-4\right)\right)\left(-5+4\right)\right)^{2}$$

Add -12 and 9 to get -3.

$$16-\left(-3\right)^{2}-\left(\left(-\left(-4\right)\right)\left(-5+4\right)\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$16-9-\left(\left(-\left(-4\right)\right)\left(-5+4\right)\right)^{2}$$

Subtract 9 from 16 to get 7.

$$7-\left(\left(-\left(-4\right)\right)\left(-5+4\right)\right)^{2}$$

The opposite of -4 is 4.

$$7-\left(4\left(-5+4\right)\right)^{2}$$

Add -5 and 4 to get -1.

$$7-\left(4\left(-1\right)\right)^{2}$$

Multiply 4 and -1 to get -4.

$$7-\left(-4\right)^{2}$$

Calculate -4 to the power of 2 and get 16.

$$7-16$$

Subtract 16 from 7 to get -9.

$$-9$$

Factor

$$-9$$