use the distributive property towrite an expression that is equivalent to 27x^2-42x+12

Question

i am trying to help my 7th grader with this problem and am stumped! please help me!

Answer 1

Factor each term and find common factors.

 

27x² - 42x + 12 = 3³x² - 2(3)7x + 2²3

 

The common factor to all three terms is 3.

 

27x² - 42x + 12 = 3(9x² - 14x + 4)

Answer 2

This is the Distributive Property in a nutshell:

3(x+5) = 3x + 15

Usually we think about it left to right, that when a number is hanging outside a pair of parentheses like that, we can distribute it, ie multiply is across all terms within the parentheses.

But we can also go from right to left! We'd say that 3x and 15 have a Greatest Common Factor of 3 and we'd factor it out so that it only needs to be represented once, outside the parentheses.

That's what we're doing with this question. Find the Greatest Common Factor between 27, 42 & 12.

• To do this, find the prime factors of each one (a factor tree is usually the common method for this). We find that:
• 27 = 3×3×3
• 42 = 2×3×7
• 12 = 2×2×3

They all have at least one 3, and nothing more, so 3 is our GCF.

We factor that out like the example equation from right to left. Basically you

• Write the GCF
• Open parentheses
• Write all the terms but with the GCF divided out (because it's outside, ready to multiply back in at a moment's notice)
• Close parentheses

Hope this helps!

-Frank