Solve (3x+8y-7)(3x+8y+7)

$$( 3 x + 8 y - 7 ) ( 3 x + 8 y + 7 )$$

Evaluate

$$\left(3x+8y\right)^{2}-49$$

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+8y and b=7.

$$\left(3x+8y\right)^{2}-7^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+8y\right)^{2}.

$$9x^{2}+48xy+64y^{2}-7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$9x^{2}+48xy+64y^{2}-49$$

Expand

$$9x^{2}+48xy+64y^{2}-49$$

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+8y and b=7.

$$\left(3x+8y\right)^{2}-7^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+8y\right)^{2}.

$$9x^{2}+48xy+64y^{2}-7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$9x^{2}+48xy+64y^{2}-49$$