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 expresiion? PLZ Help quick.

Answer 1

FIRST EXPRESSION:

- If
`b=-3`, the value of
`4b(b+1)` is
`24`

- If
`b=-2`, the value of
`4b(b+1)` is
`8`

- If
`b=10`, the value of
`4b(b+1)` is
`440`

SECOND EXPRESSION:

- If
`b=-3`, the value of
`(2b+7)(2b-8))` is
`-14`

- If
`b=-2`, the value of
`(2b+7)(2b-8))` is
`-36`

- If
`b=10`, the value of
`(2b+7)(2b-8))` is
`324`

Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.

Explanation:

Substitute the given values of "b" into each expression and evaluate.

- For the first expression
`4b(b+1)`, you get:

If
`b=-3` →
`4(-3)(-3+1)=24`

If
`b=-2` →
`4(-2)(-2+1)=8`

If
`b=10` →
`4(10)(10+1)=440`

- For the second expression
`(2b+7)(2b-8))`, you get:

If
`b=-3` →
`(2(-3)+7)(2(-3)-8)=-14`

If
`b=-2` →
`(2(-2)+7)(2(-2)-8)=-36`

If
`b=10` →
`(2(10)+7)(2(10)-8)=324`

You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.