Question Video: Factoring by Finding the Highest Common Factor

Is βˆ’9(π‘₯ βˆ’ 4) + 2(π‘₯ βˆ’ 4) = 7(π‘₯ βˆ’ 4) correct?

03:02

Video Transcript

Is negative nine multiplied by π‘₯ minus four plus two multiplied by π‘₯ minus four equal to seven multiplied by π‘₯ minus four correct?

We’re going to look at approaching this problem in two different ways. Firstly, we will look at a method that will work for all of these type of problems. And secondly, we will look at a method that’s specific to this particular question.

Our first method involves considering the left-hand side and the right-hand side of the equation separately in order to determine whether they are the same.

Expanding the first bracket or parenthesis on the left-hand side gives us negative nine π‘₯ plus 36 as negative nine multiplied by π‘₯ is negative nine π‘₯ and negative nine multiplied by negative four is positive 36. Expanding the second bracket, two multiplied by π‘₯ gives us two π‘₯ and two multiplied by negative four gives us negative eight.

Grouping the like terms negative nine π‘₯ plus two π‘₯ gives us negative seven π‘₯ and positive 36 minus eight gives us positive 28. Therefore, the left-hand side of the equation simplifies to negative seven π‘₯ plus 28.

Now, let’s consider the right-hand side of the equation. Seven multiplied by π‘₯ minus four. Well, seven multiplied by π‘₯ is seven π‘₯ and seven multiplied by negative four is negative 28. As the left-hand side is not equal to the right-hand side, we can say that the equation is not correct. This means that negative nine multiplied by π‘₯ minus four plus two multiplied by π‘₯ minus four is not equal to seven multiplied by π‘₯ minus four.

A second approach to this question would be to consider the whole equation and look for a common factor. Well, π‘₯ minus four is in all three terms. Therefore, we could divide all three of the terms by π‘₯ minus four. Dividing the first term by π‘₯ minus four gives us negative nine, dividing the second term gives just positive two, and dividing the term on the right-hand side gives us seven.

This leaves us with an equation negative nine plus two equals seven. Well, negative nine plus two is negative seven, which is not equal to the seven on the other side of the equation. Therefore, we can say once again the left-hand side is not equal to the right-hand side. This means that the statement is not correct.

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