Solve (2a + b)(a - b) + (2a - b)(a + b) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$(2a+b)(a-b)+(2a-b)(a+b)$$

Evaluate

$4a^{2}-2b^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $2a+b$ by each term of $a-b$.

$$2a^{2}-2ab+ba-b^{2}+\left(2a-b\right)\left(a+b\right)$$

Combine $-2ab$ and $ba$ to get $-ab$.

$$2a^{2}-ab-b^{2}+\left(2a-b\right)\left(a+b\right)$$

Apply the distributive property by multiplying each term of $2a-b$ by each term of $a+b$.

$$2a^{2}-ab-b^{2}+2a^{2}+2ab-ba-b^{2}$$

Combine $2ab$ and $-ba$ to get $ab$.

$$2a^{2}-ab-b^{2}+2a^{2}+ab-b^{2}$$

Combine $2a^{2}$ and $2a^{2}$ to get $4a^{2}$.

$$4a^{2}-ab-b^{2}+ab-b^{2}$$

Combine $-ab$ and $ab$ to get $0$.

$$4a^{2}-b^{2}-b^{2}$$

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

$$4a^{2}-2b^{2}$$

Expand

$4a^{2}-2b^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $2a+b$ by each term of $a-b$.

$$2a^{2}-2ab+ba-b^{2}+\left(2a-b\right)\left(a+b\right)$$

Combine $-2ab$ and $ba$ to get $-ab$.

$$2a^{2}-ab-b^{2}+\left(2a-b\right)\left(a+b\right)$$

Apply the distributive property by multiplying each term of $2a-b$ by each term of $a+b$.

$$2a^{2}-ab-b^{2}+2a^{2}+2ab-ba-b^{2}$$

Combine $2ab$ and $-ba$ to get $ab$.

$$2a^{2}-ab-b^{2}+2a^{2}+ab-b^{2}$$

Combine $2a^{2}$ and $2a^{2}$ to get $4a^{2}$.

$$4a^{2}-ab-b^{2}+ab-b^{2}$$

Combine $-ab$ and $ab$ to get $0$.

$$4a^{2}-b^{2}-b^{2}$$

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

$$4a^{2}-2b^{2}$$