Video: Evaluating Algebraic Expressions by Factoring out the GCF

Given that π‘Žπ‘ βˆ’ 4𝑐 +2π‘Ž = 12, what is the value of 12𝑐 βˆ’ 3π‘Žπ‘ βˆ’ 6π‘Ž?

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Video Transcript

Given that π‘Žπ‘ minus four 𝑐 plus two π‘Ž equals 12, what is the value of 12𝑐 minus three π‘Žπ‘ minus six π‘Ž?

Well, if we take a look at the two expressions π‘Žπ‘ minus four 𝑐 plus two π‘Ž and 12𝑐 minus three π‘Žπ‘ minus six π‘Ž, 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 π‘Žπ‘. And then we’ve got negative three π‘Žπ‘. Then we’ve got negative four 𝑐. We’ve got positive 12𝑐. And we’ve got positive two π‘Ž. And we’ve got negative six π‘Ž.

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 π‘Žπ‘ multiplied by negative three, we get negative three π‘Žπ‘. 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 π‘Ž multiplied by negative three gives us negative six π‘Ž.

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 π‘Žπ‘ minus four 𝑐 plus two π‘Ž equals 12, the value of 12𝑐 minus three π‘Žπ‘ minus six π‘Ž is negative 36.

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