Solve (4x+5y)^2-12(4x+5y).quad(HOTS)

$$( 4 x + 5 y ) ^ { 2 } - 12 ( 4 x + 5 y ) . \quad ( H O T S )$$

Evaluate

$$\left(4x+5y\right)\left(4x+5y-12\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+5y\right)^{2}.

$$16x^{2}+40xy+25y^{2}-12\left(4x+5y\right)$$

Use the distributive property to multiply -12 by 4x+5y.

$$16x^{2}+40xy+25y^{2}-48x-60y$$

Expand

$$16x^{2}+40xy-48x+25y^{2}-60y$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+5y\right)^{2}.

$$16x^{2}+40xy+25y^{2}-12\left(4x+5y\right)$$

Use the distributive property to multiply -12 by 4x+5y.

$$16x^{2}+40xy+25y^{2}-48x-60y$$