Solve (x+2y+3z)(x+2y-3z

$$( x + 2 y + 3 z ) ( x + 2 y - 3 z$$

Evaluate

$$\left(x+2y\right)^{2}-9z^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+2y+3z by each term of x+2y-3z.

$$x^{2}+2xy-3xz+2yx+4y^{2}-6yz+3zx+6zy-9z^{2}$$

Combine 2xy and 2yx to get 4xy.

$$x^{2}+4xy-3xz+4y^{2}-6yz+3zx+6zy-9z^{2}$$

Combine -3xz and 3zx to get 0.

$$x^{2}+4xy+4y^{2}-6yz+6zy-9z^{2}$$

Combine -6yz and 6zy to get 0.

$$x^{2}+4xy+4y^{2}-9z^{2}$$

Expand

$$x^{2}+4xy+4y^{2}-9z^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+2y+3z by each term of x+2y-3z.

$$x^{2}+2xy-3xz+2yx+4y^{2}-6yz+3zx+6zy-9z^{2}$$

Combine 2xy and 2yx to get 4xy.

$$x^{2}+4xy-3xz+4y^{2}-6yz+3zx+6zy-9z^{2}$$

Combine -3xz and 3zx to get 0.

$$x^{2}+4xy+4y^{2}-6yz+6zy-9z^{2}$$

Combine -6yz and 6zy to get 0.

$$x^{2}+4xy+4y^{2}-9z^{2}$$