Solve (a+b)(a-b+1)+(a-b)(a+b-1)-2b | 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

$$(a+b)(a-b+1)+(a-b)(a+b-1)-2b$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of $a+b$ by each term of $a-b+1$.

$$a^{2}-ab+a+ba-b^{2}+b+\left(a-b\right)\left(a+b-1\right)-2b$$

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

$$a^{2}+a-b^{2}+b+\left(a-b\right)\left(a+b-1\right)-2b$$

Apply the distributive property by multiplying each term of $a-b$ by each term of $a+b-1$.

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

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

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

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

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

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

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

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

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

Combine $b$ and $b$ to get $2b$.

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

Combine $2b$ and $-2b$ to get $0$.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of $a+b$ by each term of $a-b+1$.

$$a^{2}-ab+a+ba-b^{2}+b+\left(a-b\right)\left(a+b-1\right)-2b$$

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

$$a^{2}+a-b^{2}+b+\left(a-b\right)\left(a+b-1\right)-2b$$

Apply the distributive property by multiplying each term of $a-b$ by each term of $a+b-1$.

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

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

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

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

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

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

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

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

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

Combine $b$ and $b$ to get $2b$.

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

Combine $2b$ and $-2b$ to get $0$.

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