MarkFL said:I would first write the expression as:
\(\displaystyle (2ab)^2-(3(ab+c))^2\)
Now, factor as the difference of squares, and simplify. :D
RTCNTC said:The number 9 is not part of the squaring for (ab + c)^2. So, where did 3 come from? Does 3 come from the fact that 3^2 is 9? This makes sense to me if 9 were inside the parentheses for (ab + c)^2 but it's not. See what I mean?
MarkFL said:I was just rewriting that term as a perfect square:
\(\displaystyle 9(ab+c)^2=3^2(ab+c)^2=(3(ab+c))^2\)
Factoring is the process of finding the factors of a number or expression. This is important because it allows us to simplify complex equations and solve for unknown variables.
To factor a quadratic equation, you need to find two numbers that multiply to equal the constant term and add to equal the coefficient of the middle term. These numbers will be the factors of the quadratic equation.
Yes, it is possible to factor a number with more than two factors. For example, 12 can be factored as 2 x 2 x 3, where 2 and 3 are the factors.
Factoring involves finding the factors of a number or expression, while simplifying involves reducing the expression to its simplest form. Factoring is a step towards simplifying an equation.
The most common methods for factoring include grouping, difference of squares, perfect square trinomials, and trial and error. Each method is useful for factoring different types of equations.