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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

$3x^{2}+4xy-y^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $x+y$ by each term of $2x+y$.

$$2x^{2}+xy+2yx+y^{2}+\left(x+2y\right)\left(x-y\right)$$

Combine $xy$ and $2yx$ to get $3xy$.

$$2x^{2}+3xy+y^{2}+\left(x+2y\right)\left(x-y\right)$$

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

$$2x^{2}+3xy+y^{2}+x^{2}-xy+2yx-2y^{2}$$

Combine $-xy$ and $2yx$ to get $xy$.

$$2x^{2}+3xy+y^{2}+x^{2}+xy-2y^{2}$$

Combine $2x^{2}$ and $x^{2}$ to get $3x^{2}$.

$$3x^{2}+3xy+y^{2}+xy-2y^{2}$$

Combine $3xy$ and $xy$ to get $4xy$.

$$3x^{2}+4xy+y^{2}-2y^{2}$$

Combine $y^{2}$ and $-2y^{2}$ to get $-y^{2}$.

$$3x^{2}+4xy-y^{2}$$

Expand

$3x^{2}+4xy-y^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $x+y$ by each term of $2x+y$.

$$2x^{2}+xy+2yx+y^{2}+\left(x+2y\right)\left(x-y\right)$$

Combine $xy$ and $2yx$ to get $3xy$.

$$2x^{2}+3xy+y^{2}+\left(x+2y\right)\left(x-y\right)$$

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

$$2x^{2}+3xy+y^{2}+x^{2}-xy+2yx-2y^{2}$$

Combine $-xy$ and $2yx$ to get $xy$.

$$2x^{2}+3xy+y^{2}+x^{2}+xy-2y^{2}$$

Combine $2x^{2}$ and $x^{2}$ to get $3x^{2}$.

$$3x^{2}+3xy+y^{2}+xy-2y^{2}$$

Combine $3xy$ and $xy$ to get $4xy$.

$$3x^{2}+4xy+y^{2}-2y^{2}$$

Combine $y^{2}$ and $-2y^{2}$ to get $-y^{2}$.

$$3x^{2}+4xy-y^{2}$$