Evaluate
6\left(\left(x+2y\right)^{2}-9z^{2}\right)
Expand
6x^{2}+24xy+24y^{2}-54z^{2}
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\left(6x+12y-18z\right)\left(x+2y+3z\right)
Use the distributive property to multiply 6 by x+2y-3z.
6x^{2}+12xy+18xz+12yx+24y^{2}+36yz-18zx-36zy-54z^{2}
Apply the distributive property by multiplying each term of 6x+12y-18z by each term of x+2y+3z.
6x^{2}+24xy+18xz+24y^{2}+36yz-18zx-36zy-54z^{2}
Combine 12xy and 12yx to get 24xy.
6x^{2}+24xy+24y^{2}+36yz-36zy-54z^{2}
Combine 18xz and -18zx to get 0.
6x^{2}+24xy+24y^{2}-54z^{2}
Combine 36yz and -36zy to get 0.
\left(6x+12y-18z\right)\left(x+2y+3z\right)
Use the distributive property to multiply 6 by x+2y-3z.
6x^{2}+12xy+18xz+12yx+24y^{2}+36yz-18zx-36zy-54z^{2}
Apply the distributive property by multiplying each term of 6x+12y-18z by each term of x+2y+3z.
6x^{2}+24xy+18xz+24y^{2}+36yz-18zx-36zy-54z^{2}
Combine 12xy and 12yx to get 24xy.
6x^{2}+24xy+24y^{2}+36yz-36zy-54z^{2}
Combine 18xz and -18zx to get 0.
6x^{2}+24xy+24y^{2}-54z^{2}
Combine 36yz and -36zy to get 0.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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