Solve (3x-4y+5)(3x-4y-5)

$$( 3 x - 4 y + 5 ) ( 3 x - 4 y - 5 )$$

Evaluate

$$\left(3x-4y\right)^{2}-25$$

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-4y and b=5.

$$\left(3x-4y\right)^{2}-5^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4y\right)^{2}.

$$9x^{2}-24xy+16y^{2}-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9x^{2}-24xy+16y^{2}-25$$

Expand

$$9x^{2}-24xy+16y^{2}-25$$

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-4y and b=5.

$$\left(3x-4y\right)^{2}-5^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4y\right)^{2}.

$$9x^{2}-24xy+16y^{2}-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9x^{2}-24xy+16y^{2}-25$$