Video: Evaluating Algebraic Expressions by Factoring out the GCF

Video Transcript

Given that 𝑎𝑏 minus four 𝑐 plus two 𝑎 equals 12, what is the value of 12𝑐 minus three 𝑎𝑏 minus six 𝑎?

Well, if we take a look at the two expressions 𝑎𝑏 minus four 𝑐 plus two 𝑎 and 12𝑐 minus three 𝑎𝑏 minus six 𝑎, can we see any similarities? Well, what I’ve done to help us with this is put the like terms underneath each other. So we’ve got 𝑎𝑏. And then we’ve got negative three 𝑎𝑏. Then we’ve got negative four 𝑐. We’ve got positive 12𝑐. And we’ve got positive two 𝑎. And we’ve got negative six 𝑎.

Well, upon inspection, we can see that if we multiply each of the terms in the first line by negative three, it actually brings us to the terms in the second line. So if we’ve got 𝑎𝑏 multiplied by negative three, we get negative three 𝑎𝑏. If we’ve got negative four 𝑐 multiplied by negative three, we get positive 12𝑐. And that’s because a negative multiplied by a negative is a positive. And then, finally, we’ve got two 𝑎 multiplied by negative three gives us negative six 𝑎.

So therefore, if we can get to the second row from the first row by multiplying by negative three, and we know that the first row is equal to 12, then we can work out the answer of the second row or the second equation. And we get that by multiplying 12 by negative three. And this gives us an answer of negative 36. Well, we can say that, given that 𝑎𝑏 minus four 𝑐 plus two 𝑎 equals 12, the value of 12𝑐 minus three 𝑎𝑏 minus six 𝑎 is negative 36.