Solve 4(3x+y)^2-(2x+3y)^2

$$4 ( 3 x + y ) ^ { 2 } - ( 2 x + 3 y ) ^ { 2 }$$

Evaluate

$$\left(4x-y\right)\left(8x+5y\right)$$

Solution Steps

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

$$4\left(9x^{2}+6xy+y^{2}\right)-\left(2x+3y\right)^{2}$$

Use the distributive property to multiply 4 by 9x^{2}+6xy+y^{2}.

$$36x^{2}+24xy+4y^{2}-\left(2x+3y\right)^{2}$$

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

$$36x^{2}+24xy+4y^{2}-\left(4x^{2}+12xy+9y^{2}\right)$$

To find the opposite of 4x^{2}+12xy+9y^{2}, find the opposite of each term.

$$36x^{2}+24xy+4y^{2}-4x^{2}-12xy-9y^{2}$$

Combine 36x^{2} and -4x^{2} to get 32x^{2}.

$$32x^{2}+24xy+4y^{2}-12xy-9y^{2}$$

Combine 24xy and -12xy to get 12xy.

$$32x^{2}+12xy+4y^{2}-9y^{2}$$

Combine 4y^{2} and -9y^{2} to get -5y^{2}.

$$32x^{2}+12xy-5y^{2}$$

Expand

$$32x^{2}+12xy-5y^{2}$$

Solution Steps

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

$$4\left(9x^{2}+6xy+y^{2}\right)-\left(2x+3y\right)^{2}$$

Use the distributive property to multiply 4 by 9x^{2}+6xy+y^{2}.

$$36x^{2}+24xy+4y^{2}-\left(2x+3y\right)^{2}$$

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

$$36x^{2}+24xy+4y^{2}-\left(4x^{2}+12xy+9y^{2}\right)$$

To find the opposite of 4x^{2}+12xy+9y^{2}, find the opposite of each term.

$$36x^{2}+24xy+4y^{2}-4x^{2}-12xy-9y^{2}$$

Combine 36x^{2} and -4x^{2} to get 32x^{2}.

$$32x^{2}+24xy+4y^{2}-12xy-9y^{2}$$

Combine 24xy and -12xy to get 12xy.

$$32x^{2}+12xy+4y^{2}-9y^{2}$$

Combine 4y^{2} and -9y^{2} to get -5y^{2}.

$$32x^{2}+12xy-5y^{2}$$