Mathematics

# Multiply and simplify (5a + 2bc) (5a - 2bc)

#### Banaszek168

4 years ago

⇒ (a + b)(a - b) = a² - b²

Multiply and simplify :

$(5a + 2bc) (5a - 2bc) \\ =25a^2+10abc-10abc-4bc^2 \\ =25a^2-4b^2c^2$

#### BettieZumbrunnen

4 years ago

One of the tools that's great to keep in your algebra toolbox for the rest of your life is:

The product of (sum of 2 things) (difference of 2 things) = (difference in their squares).

For example:  (x + y) (x - y) = (x² - y²)

When you're trying to factor algebra expressions, it's always good to keep your
eyes open for the difference of two squares, and remember that it's going to be
(sum) x (difference) of the things that they're squares of.

Here you have (a sum) x (a difference) of the same 2 things:

(5a + 2bc) (5a - 2bc)

You can multiply them out, or just use the little tool above:

(5a)² = 25a²

(2bc)² = 4b²c²

So (their sum) x (their difference) is (25a² - 4b²c²) .