Solve 49x^2-4(y+3x)^2

$$49 x ^ { 2 } - 4 ( y + 3 x ) ^ { 2 }$$

Evaluate

$$\left(x-2y\right)\left(13x+2y\right)$$

Solution Steps

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

$$49x^{2}-4\left(y^{2}+6yx+9x^{2}\right)$$

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

$$49x^{2}-4y^{2}-24yx-36x^{2}$$

Combine 49x^{2} and -36x^{2} to get 13x^{2}.

$$13x^{2}-4y^{2}-24yx$$

Expand

$$13x^{2}-24xy-4y^{2}$$

Solution Steps

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

$$49x^{2}-4\left(y^{2}+6yx+9x^{2}\right)$$

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

$$49x^{2}-4y^{2}-24yx-36x^{2}$$

Combine 49x^{2} and -36x^{2} to get 13x^{2}.

$$13x^{2}-4y^{2}-24yx$$