Solve (3x-y+2)quad(3x-y-2)

$$( 3 x - y + 2 ) \quad ( 3 x - y - 2 )$$

Evaluate

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

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=3x-y and b=2.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-y\right)^{2}.

$$9x^{2}-6xy+y^{2}-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$9x^{2}-6xy+y^{2}-4$$

Expand

$$9x^{2}-6xy+y^{2}-4$$

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=3x-y and b=2.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-y\right)^{2}.

$$9x^{2}-6xy+y^{2}-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$9x^{2}-6xy+y^{2}-4$$