Solve 3(x^{2}-2yz+y^2)-4(x^2-y^2-3yz)+x^2=

$$3 ( x ^ { 2 } - 2 y z + y ^ { 2 } ) - 4 ( x ^ { 2 } - y ^ { 2 } - 3 y z ) + x ^ { 2 } =$$

Evaluate

$$y\left(7y+6z\right)$$

Solution Steps

Use the distributive property to multiply 3 by x^{2}-2yz+y^{2}.

$$3x^{2}-6yz+3y^{2}-4\left(x^{2}-y^{2}-3yz\right)+x^{2}$$

Use the distributive property to multiply -4 by x^{2}-y^{2}-3yz.

$$3x^{2}-6yz+3y^{2}-4x^{2}+4y^{2}+12yz+x^{2}$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}-6yz+3y^{2}+4y^{2}+12yz+x^{2}$$

Combine 3y^{2} and 4y^{2} to get 7y^{2}.

$$-x^{2}-6yz+7y^{2}+12yz+x^{2}$$

Combine -6yz and 12yz to get 6yz.

$$-x^{2}+6yz+7y^{2}+x^{2}$$

Combine -x^{2} and x^{2} to get 0.

$$6yz+7y^{2}$$

Expand

$$7y^{2}+6yz$$

Solution Steps

Use the distributive property to multiply 3 by x^{2}-2yz+y^{2}.

$$3x^{2}-6yz+3y^{2}-4\left(x^{2}-y^{2}-3yz\right)+x^{2}$$

Use the distributive property to multiply -4 by x^{2}-y^{2}-3yz.

$$3x^{2}-6yz+3y^{2}-4x^{2}+4y^{2}+12yz+x^{2}$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}-6yz+3y^{2}+4y^{2}+12yz+x^{2}$$

Combine 3y^{2} and 4y^{2} to get 7y^{2}.

$$-x^{2}-6yz+7y^{2}+12yz+x^{2}$$

Combine -6yz and 12yz to get 6yz.

$$-x^{2}+6yz+7y^{2}+x^{2}$$

Combine -x^{2} and x^{2} to get 0.

$$6yz+7y^{2}$$