2.jpeg "(ab + 3)2")
Expanding (ab + 3)²
The expression (ab + 3)² represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can use the FOIL method or the square of a binomial formula.
FOIL Method
FOIL stands for First, Outer, Inner, Last, and it helps us remember the order of multiplying the terms in the binomials.
- First: Multiply the first terms of each binomial: (ab) * (ab) = a²b²
- Outer: Multiply the outer terms: (ab) * (3) = 3ab
- Inner: Multiply the inner terms: (3) * (ab) = 3ab
- Last: Multiply the last terms: (3) * (3) = 9
Finally, combine the like terms:
(ab + 3)² = a²b² + 3ab + 3ab + 9 (ab + 3)² = a²b² + 6ab + 9
Square of a Binomial Formula
The square of a binomial formula states:
(a + b)² = a² + 2ab + b²
We can apply this formula directly to our expression:
(ab + 3)² = (ab)² + 2(ab)(3) + 3² (ab + 3)² = a²b² + 6ab + 9
Both methods lead to the same result:
(ab + 3)² = a²b² + 6ab + 9
This is the expanded form of the original expression.