To solve the expression [tex]\( (6a - 4)^2 \)[/tex] by expanding it, follow these steps:
1. Identify the expression and the use of the binomial theorem: We are given the binomial expression [tex]\( (6a - 4) \)[/tex]. The binomial theorem helps us to expand this squared expression correctly:
[tex]\[
(6a - 4)^2
\][/tex]
2. Apply the formula for squaring a binomial: The binomial theorem states that [tex]\( (x - y)^2 = x^2 - 2xy + y^2 \)[/tex]. In our case, [tex]\( x = 6a \)[/tex] and [tex]\( y = 4 \)[/tex].
3. Substitute the values into the binomial square formula:
[tex]\[
(6a - 4)^2 = (6a)^2 - 2 \cdot (6a) \cdot 4 + 4^2
\][/tex]
4. Calculate each term separately:
- First term: [tex]\((6a)^2 = 36a^2\)[/tex]
- Second term: [tex]\(-2 \cdot (6a) \cdot 4 = -48a\)[/tex]
- Third term: [tex]\(4^2 = 16\)[/tex]
5. Combine all the terms:
[tex]\[
(6a - 4)^2 = 36a^2 - 48a + 16
\][/tex]
Thus, the expanded form of [tex]\( (6a - 4)^2 \)[/tex] is:
[tex]\[
36a^2 - 48a + 16
\][/tex]
