Question

Simplify (a + b - c )(a + b + c )

Answer 1

Hello!

The answer is:

`a^(2) +b^(2) -c^(2) +2ab`

Why?

To solve the problem, we need to remember the distributive property.

The distributive property is defined by the following way:

`(a+b)(c+d)=ab+ad+bc+bd`

Also, we need to remember how to add like terms. The like terms are the terms that share the same variable and the same exponent, for example:

`x+x^(2)+x=x^(2) +2x`

We were able to add the first and the third term because they share the same variable and the same exponent.

Now, we are given the following expression to simplify:

`(a+b-c)(a+b+c)`

So, applying the distributive property and adding like terms, we have:

`(a+b-c)(a+b+c)=(a*a)+(a*b)+(a*c)+(b*a)+(b*b)+(b*c)-(c*a)-(c*b)-(c*c)\\\\(a+b-c)(a+b+c)=a^(2)+ab+ac+ba+b^(2) +bc-ac-bc-c^(2)\\\\(a+b-c)(a+b+c)=a^(2) +b^(2) -c^(2) +2ab`

Hence, we have that the given expression is equal to:

`a^(2) +b^(2) -c^(2) +2ab`

Have a nice day!

Answer 2

The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²

Explanation:

* Lets revise how to multiply two brackets with three terms

∵ (a + b - c)(a + b + c)

- Multiply the first term of the first bracket by the three terms of the

second bracket

∵ a × a = a²

∵ a × b = ab

∵ a × c = ac

- Then multiply the second term in the first bracket by the three terms

of the second bracket

∵ b × a = ba

∵ b × b = b²

∴ b × c = bc

- Then multiply the third term term in the first bracket by the three terms

of the second bracket

∵ -c × a = -ca

∵ -c × b = -cb

∵ -c × c = -c²

- Now add all these terms together

∴ a² + ab + ac + ba + b² + bc + -ca + -cb + -c²

- We have like terms lets add them

∵ ab = ba , ac = ca , bc = cb

∴ a² + (ab + ba) + (ac + -ca) + (bc + -cb) + b² + -c²

∴ a² + 2ab + 0 + 0 + b² - c²

∴ a² + 2ab + b² - c²

∴ The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²