Answer
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
[tex]x^{a}.x^{b} = x ^{a + b}[/tex]
[tex]= (2p^{2+3} - 4p^{3+1})(3p^{2} -1)[/tex]
[tex]= (2p^{5} - 4p^{4})(3p^{2} -1)[/tex]
Again multiply the terms
[tex]= (2p^{5}\times 3p^{2} - 4p^{4}\times 3p^{2} - 2p^{5} + 4p^{4})[/tex]
[tex]= (6p^{5+2} - 12p^{4+2} - 2p^{5} + 4p^{4})[/tex]
[tex]= (6p^{7} - 12p^{6} - 2p^{5} + 4p^{4})[/tex]
Therefore the option (C) is correct.