Mathematics: 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.

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Tina was asked to determine the possible dimensions

taleiayarbough4544

07.02.2022

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

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