Q:

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 expresiion? PLZ Help quick.

Accepted Solution

A:
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.