Solve left(2x-6y+8right)left(2x-6y-8right)

$$\left( 2x-6y+8 \right) \left( 2x-6y-8 \right)$$

Evaluate

$$4\left(\left(x-3y\right)^{2}-16\right)$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=2x-6y and b=8.

$$\left(2x-6y\right)^{2}-8^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-6y\right)^{2}.

$$4x^{2}-24xy+36y^{2}-8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$4x^{2}-24xy+36y^{2}-64$$

Expand

$$4x^{2}-24xy+36y^{2}-64$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=2x-6y and b=8.

$$\left(2x-6y\right)^{2}-8^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-6y\right)^{2}.

$$4x^{2}-24xy+36y^{2}-8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$4x^{2}-24xy+36y^{2}-64$$