Question

What is the product of (p3)(2p2 - 4p)(3p2 - 1)?

A) 6p7 + 4p4

B) 6p7- 2p5 - 12p5 + 4p3

C) 6p7 - 12p6 - 2p5 + 4p4

D) 6p12 - 14p6 + 4p3

Answer 1

The answer is actually C

Answer 2

Find out the product of ( p³)(2p² - 4p)(3p² - 1) .

To prove

The expression given in the question

= ( p³) × (2p² - 4p) × (3p² - 1)

First multiply first two terms

= ( p³ × 2p² - p³ × 4p)(3p² - 1)

Now using the exponent property

`x^(a).x^(b) = x ^(a + b)`

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

`= (2p^(5) - 4p^(4))(3p^(2) -1)`

Again multiply the terms

`= (2p^(5)* 3p^(2) - 4p^(4)* 3p^(2) - 2p^(5) + 4p^(4))`

`= (6p^(5+2) - 12p^(4+2) - 2p^(5) + 4p^(4))`

`= (6p^(7) - 12p^(6) - 2p^(5) + 4p^(4))`

Therefore the option (C) is correct.