Mathematics
09.05.2023 19:37
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Consider 18x4y + 3x3y2 – 39x²y3 + 12x2y4 as an expression in x. xy x^y 3x^2y 3xy

Consider 18x4y + 3x3y2 – 39x²y3 + 12x2y4 as an expression in x. xy
x^y
3x^2y
3xy

Part A
What is the greatest common factor (GCF) for the four terms?

Part B

what is the leading coefficient of the expression ?

3
4
12
8
Show Answers
jcastronakaya
jcastronakaya
4,9(33 marks)

XD

Step-by-step explanation:

trillsmith
trillsmith
4,6(53 marks)

A. \frac{1}{(r+1)\cdot (r-2)}

Step-by-step explanation:

We have been given an expression \frac{r+2}{4r^2+5r+1}\cdot \frac{4r+1}{r^2-4}. We are asked to simplify our given expression.    

We will factor the denominators of both fractions as shown below:    

4r^2+5r+1

4r^2+4r+r+1 Splitting the middle term.

(4r^2+4r)+(r+1)  Making groups.

4r(r+1)+(r+1)  Factor out 4r from 1st group.

4r(r+1)+1(r+1)  Factor out 1 from 2nd group.

(4r+1)(r+1)

Using difference of squares we will factor the 2nd denominator as:

r^2-4=r^2-2^2=(r+2)(r-2)

Substituting these values in our given problem we will get,

\frac{r+2}{(4r+1)(r+1)}\cdot \frac{4r+1}{(r+2)(r-2)}

After cancelling out terms we will get,

\frac{1}{(r+1)}\cdot \frac{1}{(r-2)}

\frac{1}{(r+1)\cdot (r-2)}

Therefore, option A is the correct choice.

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