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An expression is shown below: 3pf^2 - 21p^2f + 6pf - 42p^2. Rewrite the expression completely factored. Show the steps of your work.

Respuesta :

First find the GCF - this is 3p which we take out:-

= 3p(f^2 - 7pf + 2f - 14p)

we can factor the terms in the parentheses by grouping:-

= 3p [f(f - 7p) + 2(f - 7p)]

= 3p(f - 7p)( f + 2) answer

The final expression will be equal to 3p(f - 7p)( f + 2).

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression will be solved as below:-

First find the GCF - this is 3p which we take out:-

E= 3p(f² - 7pf + 2f - 14p)

Factor the terms in the parentheses by grouping:-

E= 3p [f(f - 7p) + 2(f - 7p)]

E= 3p(f - 7p)( f + 2)

Therefore, the final expression will be equal to 3p(f - 7p)( f + 2).

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