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(4x+7)^2

2 min read Jun 16, 2024
(4x+7)^2

Expanding the Square of a Binomial: (4x+7)^2

The expression (4x+7)^2 represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can use the FOIL method (First, Outer, Inner, Last) or simply apply the distributive property.

Expanding using FOIL

  • First: Multiply the first terms of each binomial: (4x)(4x) = 16x²
  • Outer: Multiply the outer terms: (4x)(7) = 28x
  • Inner: Multiply the inner terms: (7)(4x) = 28x
  • Last: Multiply the last terms: (7)(7) = 49

Now, add all the results together: 16x² + 28x + 28x + 49

Combining the like terms, we get: 16x² + 56x + 49

Expanding using Distributive Property

We can also apply the distributive property twice:

  1. (4x + 7) * (4x + 7)
  2. 4x(4x + 7) + 7(4x + 7)
  3. 16x² + 28x + 28x + 49
  4. 16x² + 56x + 49

Therefore, the expanded form of (4x+7)^2 is 16x² + 56x + 49.

Summary

Expanding (4x+7)^2 results in a trinomial: 16x² + 56x + 49. This can be achieved by using either the FOIL method or the distributive property. Both methods arrive at the same answer.

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