Solve 16x^2-(5y+z)^2

$$16 x ^ { 2 } - ( 5 y + z ) ^ { 2 }$$

Evaluate

$$-\left(5y+z\right)^{2}+16x^{2}$$

Solution Steps

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

$$16x^{2}-\left(25y^{2}+10yz+z^{2}\right)$$

To find the opposite of 25y^{2}+10yz+z^{2}, find the opposite of each term.

$$16x^{2}-25y^{2}-10yz-z^{2}$$

Expand

$$16x^{2}-25y^{2}-10yz-z^{2}$$

Solution Steps

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

$$16x^{2}-\left(25y^{2}+10yz+z^{2}\right)$$

To find the opposite of 25y^{2}+10yz+z^{2}, find the opposite of each term.

$$16x^{2}-25y^{2}-10yz-z^{2}$$