(y%2B2)-(3y%2B4)(2y%2B1).jpeg "(6y-1)(y+2) (3y+4)(2y+1)")
Expanding and Simplifying the Expression (6y-1)(y+2) (3y+4)(2y+1)
This article will guide you through the process of expanding and simplifying the given expression: (6y-1)(y+2) (3y+4)(2y+1).
Step 1: Expanding the First Two Binomials
We start by expanding the first two binomials using the FOIL method (First, Outer, Inner, Last):
- (6y-1)(y+2)
- First: 6y * y = 6y²
- Outer: 6y * 2 = 12y
- Inner: -1 * y = -y
- Last: -1 * 2 = -2
Combining the terms, we get: 6y² + 11y - 2
Step 2: Expanding the Second Two Binomials
Next, we expand the second pair of binomials using the same FOIL method:
- (3y+4)(2y+1)
- First: 3y * 2y = 6y²
- Outer: 3y * 1 = 3y
- Inner: 4 * 2y = 8y
- Last: 4 * 1 = 4
Combining the terms, we get: 6y² + 11y + 4
Step 3: Combining the Expanded Expressions
Now we have: (6y² + 11y - 2)(6y² + 11y + 4)
This is essentially the product of two trinomials. To expand this, we can use the distributive property, multiplying each term of the first trinomial by each term of the second trinomial:
- 6y² (6y² + 11y + 4) = 36y⁴ + 66y³ + 24y²
- 11y (6y² + 11y + 4) = 66y³ + 121y² + 44y
- -2 (6y² + 11y + 4) = -12y² - 22y - 8
Step 4: Combining Like Terms
Finally, we combine all the terms we obtained in the previous step:
36y⁴ + 66y³ + 24y² + 66y³ + 121y² + 44y - 12y² - 22y - 8
Simplifying by combining like terms:
36y⁴ + 132y³ + 133y² + 22y - 8
Conclusion
Therefore, the expanded and simplified form of the expression (6y-1)(y+2) (3y+4)(2y+1) is 36y⁴ + 132y³ + 133y² + 22y - 8.