Solve (a + b - c)(a - b + c) | 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

$$(a+b-c)\times(a-b+c)$$

Evaluate

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

Solution Steps

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

$$a^{2}-ab+ac+ba-b^{2}+bc-ca+cb-c^{2}$$

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

$$a^{2}+ac-b^{2}+bc-ca+cb-c^{2}$$

Combine $ac$ and $-ca$ to get $0$.

$$a^{2}-b^{2}+bc+cb-c^{2}$$

Combine $bc$ and $cb$ to get $2bc$.

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

Expand

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

Solution Steps

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

$$a^{2}-ab+ac+ba-b^{2}+bc-ca+cb-c^{2}$$

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

$$a^{2}+ac-b^{2}+bc-ca+cb-c^{2}$$

Combine $ac$ and $-ca$ to get $0$.

$$a^{2}-b^{2}+bc+cb-c^{2}$$

Combine $bc$ and $cb$ to get $2bc$.

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