Question

What is the expression in factored form? 9x^2 - 12x + 4

Answer 1

Answer:

C. (3x - 2)²

Step-by-step explanation:

The square of a binomial can be written as (a + b)². If you expand this formula, you get

(a + b)(a + b). Use F.O.I.L. to multiply this out..

F - stands for 'Firsts' (the first values in each set of parenthesis)

O - stands for 'Outsides' ( the first value in the first set of parenthesis, and the  

second value in the second set of parenthesis)

I - stands for 'Insides' ( the second value in the first set of parenthesis, and  

the first value in the second set of parenthesis)

L - stands for 'Lasts' ( the second value in each set of parenthesis)

This is the order you multiply them in...so we get

F - a² (a times a)

O - ab  

I - ba (which we rewrite as ab, since order doesn't matter when multiplying)

L - b²

We add them together to get a² + ab + ab + b²

which simplifies to a² + 2ab + b²

Read this as, the square of the first term in the parenthesis (a²), plus twice the product of the terms (2ab is twice the product of a and b), plus the square of the last term in the parenthesis)

So to solve this we need to factor  9x² - 12x + 4

Look at the bold paragraph above and work backwards.  

Take the square root of the term 9x², which is 3x. That goes in the first value of the parenthesis, so we have

(3x + b)²  

We know that -12x is twice the product of the two terms, so we divide by 2 to see the product of the two terms.

-12x/2 = -6x,  

We know one term, so divide -6x by the first term, 3x, to find the second term.

-6x/3x = -2

So the last term in our set of parenthesis is -2, so we have

(3x - 2)²  

Answer 2

The answer is (3x-2)^2