Question

Someone please help me with this math problem! :(

Answer 1

area of a parallelogram=base x heigth
Data:
base=(2x+3)
heigth=(ax+5)
area of this parallelogram=8x²+bx+15

Therefore:
8x²+bx+15=(2x+3)(ax+5)
8x²+bx+15=2ax²+10x+3ax+15
8x²+bx+15=2ax²+(10+3a)x+15

Then:
8x²=2ax²
a=(8x²)/(2x²)=4

bx=(10+3(4))x
bx=(10+12)x
b=22x/x=22

Answer: a=4 and b=22.

Answer 2

The formula for this area is basexheight so you have to mutiply (2x+3)x(ax+5) and this multiplication must be equal to 8x^2+bx+15. If you do the multiply and then equalization you will get 2ax^2+10x+3ax+15 = 8x^2+bx+15.
Now is easy to see that 2ax^2 must be equal to 8x^2 so 2a=8 you solve for a and you get a=4. The same step for b you have 10x+3ax= bx so 10+3a=b as you know now a is 4 so 10+12=b you solve for b and you get b=22.
The answer is a=4 and b=22