Solve 25(m+3n)^2-40(m+3n)+16

$$25 ( m + 3 n ) ^ { 2 } - 40 ( m + 3 n ) + 16$$

Evaluate

$$\left(5m+15n-4\right)^{2}$$

Solution Steps

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

$$25\left(m^{2}+6mn+9n^{2}\right)-40\left(m+3n\right)+16$$

Use the distributive property to multiply 25 by m^{2}+6mn+9n^{2}.

$$25m^{2}+150mn+225n^{2}-40\left(m+3n\right)+16$$

Use the distributive property to multiply -40 by m+3n.

$$25m^{2}+150mn+225n^{2}-40m-120n+16$$

Expand

$$25m^{2}+150mn-40m+225n^{2}-120n+16$$

Solution Steps

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

$$25\left(m^{2}+6mn+9n^{2}\right)-40\left(m+3n\right)+16$$

Use the distributive property to multiply 25 by m^{2}+6mn+9n^{2}.

$$25m^{2}+150mn+225n^{2}-40\left(m+3n\right)+16$$

Use the distributive property to multiply -40 by m+3n.

$$25m^{2}+150mn+225n^{2}-40m-120n+16$$