Question Video: Evaluating Algebraic Expressions by Factoring Out the Highest Common Factor | Nagwa Question Video: Evaluating Algebraic Expressions by Factoring Out the Highest Common Factor | Nagwa

# Question Video: Evaluating Algebraic Expressions by Factoring Out the Highest Common Factor

If 3π β 2π = 5 and 2π + π = β3, what is the value of 6π+3π β 3π + 2π?

01:50

### Video Transcript

If three π minus two π is equal to five and two π plus π is equal to negative three, what is the value of six π plus three π minus three π plus two π?

In this question, weβve been given the value of two algebraic expressions. What weβre absolutely not going to do is individually try and work out the value of π, π, π, and π. Thereβs simply not enough information to do so. Instead, weβll try to find a way to relate these two expressions to the third expression in our question. Thatβs six π plus three π minus three π plus two π.

Now if we look carefully, we might notice that six π plus three π looks a little bit like the expression two π plus π. And negative three π plus two π has something in common with the expression three π minus two π. In fact, if we factor three from the expression six π plus three π, we see we can write it as three times two π plus π. But of course we already saw that two π plus π is equal to negative three. So we can write this as three times negative three, which is simply negative nine.

Now this next step isnβt so obvious. But weβre going to factor negative three π plus two π. Thatβs the second half of our third expression. Weβre going to factor negative one. When we divide negative three π by negative one, we get three π. And when we divide two π by negative one, we get negative two π.

But of course, the question tells us that three π minus two π is five. So this becomes negative one times five, which is negative five. Weβll rewrite the third expression just slightly. Weβll write it as six π plus three π plus negative three π plus two π. Weβve just calculated the value of six π plus three π. Itβs negative nine. Similarly, we calculated the value of negative three π plus two π. Itβs negative five. So six π plus three π minus three π plus two π is the same as negative nine plus negative five, which is equal to negative 14.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions