Question

Tina was asked to determine the possible dimensions of a given rectangle whose area is 12a4b3-18a6b3-72a7b3. Tina stated that the possible dimensions (written as a product) of the given rectangle were: 3a4b3(4-6a2-24a3). Do you agree or disagree with Tina? Explain your answer.

Answer 1

Tina is correct

Explanation:

Given

`Area = 12a^4b^3 - 18a^6b^3 - 72a^7b^3`

Required

State if
`3a^4b^3(4-6a^2-24a^3)` is a possible dimension

To do this, we simply expand
`3a^4b^3(4-6a^2-24a^3)`

`3a^4b^3(4-6a^2-24a^3)`

`3a^4b^3 * 4-3a^4b^3 * 6a^2-3a^4b^3 * 24a^3`

`12a^4b^3 - 18a^(4+2)b^3 * -72a^(4+3)b^3`

`12a^4b^3 - 18a^(6)b^3 * -72a^(7)b^3`

By comparison, the result of the expansion

`12a^4b^3 - 18a^(6)b^3 * -72a^(7)b^3`

and the given expression

`Area = 12a^4b^3 - 18a^6b^3 - 72a^7b^3`

are the same.

Hence, Tina is correct