Question

Which of the following is equivalent to (p3)(2p2 - 4p)(3p2 - 1)?

A) (p3)(6p4 - 12p3 - 2p2 + 4p)
B) (p3)(6p4 + 4p)
C) (2p6 - 4p3)(3p2 - 1)
D) (2p5 - 4p4)(3p5 - p3)

Answer 1

(p³)(2p² - 4p)(3p² - 1) = (p³)(2p²*3p² - 4p*3p² - 1*2p² - 4p*(-1)) =
= (p³)(6p⁴ - 12p³ - 2p² + 4p)

Answer: A)

Answer 2

Answer: Option 'A' is correct.

Explanation:

Since we have given that

`(p^3)(2p^2-4p)(3p^2-1)`

Now, we will solve the last two terms using "Product of polynomials":

`\left(2p^2-4p\right)\left(3p^2-1\right)\\\\\text{Using this :}\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\a=2p^2,\:b=-4p,\:c=3p^2,\:d=-1\\\\=2p^2\cdot \:3p^2+2p^2\left(-1\right)+\left(-4p\right)\cdot \:3p^2+\left(-4p\right)\left(-1\right)`

So, at last it becomes:

`\left(p^3\right)\left(6p^4-12p^3-2p^2+4p\right)`

Hence, Option 'A' is correct.