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

Answer:

Tina is correct

Step-by-step 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