(ab + 3)2

2 min read Jun 16, 2024
(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.

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