Solve 9x^2-4(y+2x)^2

$$9 x ^ { 2 } - 4 ( y + 2 x ) ^ { 2 }$$

Evaluate

$$-\left(x+2y\right)\left(7x+2y\right)$$

Solution Steps

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

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

Use the distributive property to multiply -4 by y^{2}+4yx+4x^{2}.

$$9x^{2}-4y^{2}-16yx-16x^{2}$$

Combine 9x^{2} and -16x^{2} to get -7x^{2}.

$$-7x^{2}-4y^{2}-16yx$$

Expand

$$-7x^{2}-16xy-4y^{2}$$

Solution Steps

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

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

Use the distributive property to multiply -4 by y^{2}+4yx+4x^{2}.

$$9x^{2}-4y^{2}-16yx-16x^{2}$$

Combine 9x^{2} and -16x^{2} to get -7x^{2}.

$$-7x^{2}-4y^{2}-16yx$$