Factor -5a^2b + 10ab^2 - 20b + 25a^3b

2 answers:

6 0

For this case we have the following expression:
-5a ^ 2b + 10ab ^ 2 - 20b + 25a ^ 3b
We observe that the term 5b is repeated throughout the expression,
therefore it is a common factor.
So, factoring we have:
5b (-a ^ 2 + 2ab - 4 + 5a ^ 3)
Then, rewriting we have:
5b (a ^ 2 (5a-1) + 2ab-4)
Answer:
The factored expression is given by:
5b (a ^ 2 (5a-1) + 2ab-4)

marysya [2.9K]2 years ago

4 0

Factor out the GCF, which is 5b, and you get: 5b(5a^3-a^2+2ab-4)

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Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$