Question

Consider the two expressions 4b(b+1) and (2b+7)(2b-8). Compare their values if b=-3, b=-2, and if b=10. Is it true that for an value of b the value of the first expression is greater than the value of the second expression

Answer 1

If b = -3, then 4b(b+1) > (2b+7)(2b-8).

If b = -2, then 4b(b+1) > (2b+7)(2b-8).

If b = 10, then 4b(b+1) > (2b+7)(2b-8).

Not true for any value of b the value of 1st expression is greater than 2nd

Explanation:

Substitute b into expressions and check if true

4(-3)((-3)+1) > (2(-3)+7)(2(-3)-8)

-12(-2) > (-6+7)(-6-8)

24 > (1)(-14)

24 > -14, do rest, there are certain values value of 1st isn't greater than 2nd, you can find these values by simplifying

Answer 2

If b=-3 then the first expression is equal to 24 and the second expression is equal to -14.

If b=-2 then the first expression is equal to 8 and the second expression is equal to -36.

If b=10 then the first expression is equal to 440 and the second expression is equal to 324.

Yes, it is true.

Explanation:

b=-3:

4b(b+1)=4(-3)(-3+1)=-12(-2)=24

(2b+7)(2b-8)=(2(-3)+7)(2(-3)-8)=(-6+7)(-6-8)=1(-14)=-14

b=-2:

4b(b+1)=4(-2)(-2+1)=-8(-1)=8

(2b+7)(2b-8)=(2(-2)+7)(2(-2)-8)=(-4+7)(-4-8)=3(-12)=-36

b=10:

4b(b+1)=4(10)(10+1)=40(11)=440

(2b+7)(2b-8)=(2(10)+7)(2(10)-8)=(20+7)(20-8)=27(12)=324