Solve 2y^2?(-6)^2-3(-6)(-3)-2(-3)^2

$$2 y ^ { 2 } ? ( - 6 ) ^ { 2 } - 3 ( - 6 ) ( - 3 ) - 2 ( - 3 ) ^ { 2 }$$

Evaluate

$$72\left(y^{2}-1\right)$$

Solution Steps

Calculate -6 to the power of 2 and get 36.

$$2y^{2}\times 36-3\left(-6\right)\left(-3\right)-2\left(-3\right)^{2}$$

Multiply 2 and 36 to get 72.

$$72y^{2}-3\left(-6\right)\left(-3\right)-2\left(-3\right)^{2}$$

Multiply 3 and -6 to get -18.

$$72y^{2}-\left(-18\left(-3\right)\right)-2\left(-3\right)^{2}$$

Multiply -18 and -3 to get 54.

$$72y^{2}-54-2\left(-3\right)^{2}$$

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

$$72y^{2}-54-2\times 9$$

Multiply 2 and 9 to get 18.

$$72y^{2}-54-18$$

Subtract 18 from -54 to get -72.

$$72y^{2}-72$$

Factor

$$72\left(y-1\right)\left(y+1\right)$$

Solution Steps

Factor out 18.

$$18\left(4y^{2}-4\right)$$

Consider 4y^{2}-3-1. Multiply and combine like terms.

$$4y^{2}-4$$

Consider 4y^{2}-4. Factor out 4.

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

Consider y^{2}-1. Rewrite y^{2}-1 as y^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-1\right)\left(y+1\right)$$

Rewrite the complete factored expression.

$$72\left(y+1\right)\left(y-1\right)$$

Simplify.

$$72\left(y-1\right)\left(y+1\right)$$