Solve 49(x+y)^2-16(x-y)^2

$$49 ( x + y ) ^ { 2 } - 16 ( x - y ) ^ { 2 }$$

Evaluate

$$\left(3x+11y\right)\left(11x+3y\right)$$

Solution Steps

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

$$49\left(x^{2}+2xy+y^{2}\right)-16\left(x-y\right)^{2}$$

Use the distributive property to multiply 49 by x^{2}+2xy+y^{2}.

$$49x^{2}+98xy+49y^{2}-16\left(x-y\right)^{2}$$

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

$$49x^{2}+98xy+49y^{2}-16\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -16 by x^{2}-2xy+y^{2}.

$$49x^{2}+98xy+49y^{2}-16x^{2}+32xy-16y^{2}$$

Combine 49x^{2} and -16x^{2} to get 33x^{2}.

$$33x^{2}+98xy+49y^{2}+32xy-16y^{2}$$

Combine 98xy and 32xy to get 130xy.

$$33x^{2}+130xy+49y^{2}-16y^{2}$$

Combine 49y^{2} and -16y^{2} to get 33y^{2}.

$$33x^{2}+130xy+33y^{2}$$

Expand

$$33x^{2}+130xy+33y^{2}$$

Solution Steps

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

$$49\left(x^{2}+2xy+y^{2}\right)-16\left(x-y\right)^{2}$$

Use the distributive property to multiply 49 by x^{2}+2xy+y^{2}.

$$49x^{2}+98xy+49y^{2}-16\left(x-y\right)^{2}$$

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

$$49x^{2}+98xy+49y^{2}-16\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -16 by x^{2}-2xy+y^{2}.

$$49x^{2}+98xy+49y^{2}-16x^{2}+32xy-16y^{2}$$

Combine 49x^{2} and -16x^{2} to get 33x^{2}.

$$33x^{2}+98xy+49y^{2}+32xy-16y^{2}$$

Combine 98xy and 32xy to get 130xy.

$$33x^{2}+130xy+49y^{2}-16y^{2}$$

Combine 49y^{2} and -16y^{2} to get 33y^{2}.

$$33x^{2}+130xy+33y^{2}$$