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

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

Evaluate

$\left(2a-1\right)\left(2b-1\right)$

Solution Steps

Use the distributive property to multiply $a+b-2$ by $a+b$ and combine like terms.

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

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-b\right)^{2}$.

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

To find the opposite of $a^{2}-2ab+b^{2}$, find the opposite of each term.

$$a^{2}+2ab+b^{2}-2a-2b-a^{2}+2ab-b^{2}+1$$

Combine $a^{2}$ and $-a^{2}$ to get $0$.

$$2ab+b^{2}-2a-2b+2ab-b^{2}+1$$

Combine $2ab$ and $2ab$ to get $4ab$.

$$4ab+b^{2}-2a-2b-b^{2}+1$$

Combine $b^{2}$ and $-b^{2}$ to get $0$.

$$4ab-2a-2b+1$$

Expand

$4ab-2a-2b+1$

Solution Steps

Use the distributive property to multiply $a+b-2$ by $a+b$ and combine like terms.

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

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-b\right)^{2}$.

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

To find the opposite of $a^{2}-2ab+b^{2}$, find the opposite of each term.

$$a^{2}+2ab+b^{2}-2a-2b-a^{2}+2ab-b^{2}+1$$

Combine $a^{2}$ and $-a^{2}$ to get $0$.

$$2ab+b^{2}-2a-2b+2ab-b^{2}+1$$

Combine $2ab$ and $2ab$ to get $4ab$.

$$4ab+b^{2}-2a-2b-b^{2}+1$$

Combine $b^{2}$ and $-b^{2}$ to get $0$.

$$4ab-2a-2b+1$$