(3x%2B2)(2x%2B1)(3x%2B2).jpeg "(2x+1)(3x+2)(2x+1)(3x+2)")
Expanding and Simplifying (2x+1)(3x+2)(2x+1)(3x+2)
This expression involves multiplying four factors, two of which are identical: (2x+1) and (3x+2). We can simplify this process by combining the identical factors.
Step 1: Combine identical factors
Since we have two identical factors, we can rewrite the expression as:
(2x+1)² (3x+2)²
Step 2: Expand the squares
We can expand the squares using the FOIL method (First, Outer, Inner, Last) or by recognizing the pattern (a+b)² = a² + 2ab + b².
(2x+1)² = (2x)² + 2(2x)(1) + (1)² = 4x² + 4x + 1
(3x+2)² = (3x)² + 2(3x)(2) + (2)² = 9x² + 12x + 4
Step 3: Multiply the expanded factors
Now we need to multiply the two expanded expressions:
(4x² + 4x + 1)(9x² + 12x + 4)
This multiplication involves multiplying each term in the first expression by each term in the second expression. It's a bit tedious but straightforward.
Step 4: Simplify the final expression
After performing the multiplication and combining like terms, the simplified expression is:
36x⁴ + 96x³ + 82x² + 28x + 4
Final answer
Therefore, the expanded and simplified form of (2x+1)(3x+2)(2x+1)(3x+2) is 36x⁴ + 96x³ + 82x² + 28x + 4.