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

Yes, I agree with Tina

Explanation:

The rectangle area which is 12a⁴b³-18a⁶b³-72a⁷b³. To get Tina's answer, we factorize the area of the rectangle which is 12a⁴b³-18a⁶b³-72a⁷b³. Now, there is a common factor of 3a⁴b³ in each term. So, we have that

12a⁴b³-18a⁶b³-72a⁷b³ = 3a⁴b³ × 4 - 3a⁴b³ × 6a² - 3a⁴b³ × 24a³.

Factorizing out 3a⁴b³, we have

3a⁴b³(4 - 6a² - 24a³).

So, the area of the rectangle given as a product is 3a⁴b³(4 - 6a² - 24a³).

Since this is the answer for the area of the rectangle Tina got, Yes, I agree with Tina since we have the same answer.