Certainly! Let's simplify the given mathematical expression step by step. The expression is:
[tex]\[ c^2 + 2cd + d^2 \][/tex]
### Step 1: Identify the pattern
At first glance, the given expression resembles the expansion of a binomial square. Recall that the expansion of [tex]\((a + b)^2\)[/tex] using the binomial theorem is:
[tex]\[ (a + b)^2 = a^2 + 2ab + b^2 \][/tex]
### Step 2: Compare with the binomial expansion
In our expression [tex]\( c^2 + 2cd + d^2 \)[/tex]:
- [tex]\( c^2 \)[/tex] can be compared to [tex]\( a^2 \)[/tex]
- [tex]\( 2cd \)[/tex] can be compared to [tex]\( 2ab \)[/tex]
- [tex]\( d^2 \)[/tex] can be compared to [tex]\( b^2 \)[/tex]
### Step 3: Writing it as a square of a binomial
Given that the provided expression fits this pattern well, we can rewrite it in a more compact form. By carefully examining each term, we confirm that we indeed have the square of a sum of two terms.
### Final step: Rewriting the expression
Notice that the terms correspond directly to [tex]\((c + d)^2\)[/tex]:
[tex]\[ c^2 + 2cd + d^2 = (c + d)^2 \][/tex]
So, the simplified form of the expression [tex]\( c^2 + 2cd + d^2 \)[/tex] is:
[tex]\[ (c + d)^2 \][/tex]
Thus, the given expression simplifies to [tex]\((c + d)^2\)[/tex], which is the final result.
