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(12x2 + 7y3)(4x2 + 7y3)

2 min read Jun 16, 2024
(12x2 + 7y3)(4x2 + 7y3)

Expanding the Expression (12x² + 7y³) (4x² + 7y³)

This article will demonstrate how to expand the expression (12x² + 7y³) (4x² + 7y³) using the FOIL method.

Understanding FOIL

FOIL stands for First, Outer, Inner, Last. It's a mnemonic device that helps remember the steps involved in expanding a product of two binomials. Let's break it down:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomial.

Applying FOIL to our Expression

Let's apply the FOIL method to our expression:

  1. First: (12x²) * (4x²) = 48x⁴
  2. Outer: (12x²) * (7y³) = 84x²y³
  3. Inner: (7y³) * (4x²) = 28x²y³
  4. Last: (7y³) * (7y³) = 49y⁶

Now, combine all the terms:

48x⁴ + 84x²y³ + 28x²y³ + 49y⁶

Finally, simplify by combining like terms:

48x⁴ + 112x²y³ + 49y⁶

Conclusion

The expanded form of (12x² + 7y³) (4x² + 7y³) is 48x⁴ + 112x²y³ + 49y⁶. This process, using the FOIL method, allows us to multiply binomials efficiently and accurately.

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