Evaluate
-3x\left(3x+9z+2\right)-\left(4z+13\right)^{2}
Expand
-9x^{2}-27xz-6x-16z^{2}-104z-169
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3x\left(-9z-3x-2\right)-\left(3+4z+10\right)^{2}
Combine 4x and -7x to get -3x.
-27xz-9x^{2}-6x-\left(3+4z+10\right)^{2}
Use the distributive property to multiply 3x by -9z-3x-2.
-27xz-9x^{2}-6x-\left(13+4z\right)^{2}
Add 3 and 10 to get 13.
-27xz-9x^{2}-6x-\left(169+104z+16z^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(13+4z\right)^{2}.
-27xz-9x^{2}-6x-169-104z-16z^{2}
To find the opposite of 169+104z+16z^{2}, find the opposite of each term.
3x\left(-9z-3x-2\right)-\left(3+4z+10\right)^{2}
Combine 4x and -7x to get -3x.
-27xz-9x^{2}-6x-\left(3+4z+10\right)^{2}
Use the distributive property to multiply 3x by -9z-3x-2.
-27xz-9x^{2}-6x-\left(13+4z\right)^{2}
Add 3 and 10 to get 13.
-27xz-9x^{2}-6x-\left(169+104z+16z^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(13+4z\right)^{2}.
-27xz-9x^{2}-6x-169-104z-16z^{2}
To find the opposite of 169+104z+16z^{2}, find the opposite of each term.
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