Answer:
FIRST EXPRESSION:
- If [tex]b=-3[/tex], the value of [tex]4b(b+1)[/tex] is [tex]24[/tex]
- If [tex]b=-2[/tex], the value of [tex]4b(b+1)[/tex] is [tex]8[/tex]
- If [tex]b=10[/tex], the value of [tex]4b(b+1)[/tex] is [tex]440[/tex]
SECOND EXPRESSION:
- If [tex]b=-3[/tex], the value of [tex](2b+7)(2b-8))[/tex] is [tex]-14[/tex]
- If [tex]b=-2[/tex], the value of [tex](2b+7)(2b-8))[/tex] is [tex]-36[/tex]
- If [tex]b=10[/tex], the value of [tex](2b+7)(2b-8))[/tex] is [tex]324[/tex]
Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.
Step-by-step explanation:
Substitute the given values of "b" into each expression and evaluate.
- For the first expression [tex]4b(b+1)[/tex], you get:
If [tex]b=-3[/tex] → [tex]4(-3)(-3+1)=24[/tex]
If [tex]b=-2[/tex] → [tex]4(-2)(-2+1)=8[/tex]
If [tex]b=10[/tex] → [tex]4(10)(10+1)=440[/tex]
- For the second expression [tex](2b+7)(2b-8))[/tex], you get:
If [tex]b=-3[/tex] → [tex](2(-3)+7)(2(-3)-8)=-14[/tex]
If [tex]b=-2[/tex] → [tex](2(-2)+7)(2(-2)-8)=-36[/tex]
If [tex]b=10[/tex] → [tex](2(10)+7)(2(10)-8)=324[/tex]
You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.
