(-6x-7y^2)^2

Jasonbradley

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Jun 16, 2024

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Expanding the Square: (-6x - 7y^2)^2

Squaring a binomial like (-6x - 7y^2)^2 involves using the FOIL method or recognizing the pattern of (a + b)^2. Let's break down both approaches:

Using the FOIL Method:

FOIL stands for First, Outer, Inner, Last and helps us multiply two binomials.

1. First: Multiply the first terms of each binomial: (-6x) * (-6x) = 36x^2
2. Outer: Multiply the outer terms: (-6x) * (-7y^2) = 42xy^2
3. Inner: Multiply the inner terms: (-7y^2) * (-6x) = 42xy^2
4. Last: Multiply the last terms: (-7y^2) * (-7y^2) = 49y^4

Finally, combine the terms:

36x^2 + 42xy^2 + 42xy^2 + 49y^4 = 36x^2 + 84xy^2 + 49y^4

Recognizing the Pattern:

The expression (a + b)^2 expands to a^2 + 2ab + b^2. We can apply this to our problem:

• a = -6x
• b = -7y^2

Substituting:

(-6x)^2 + 2(-6x)(-7y^2) + (-7y^2)^2 = 36x^2 + 84xy^2 + 49y^4

Conclusion

Both methods lead to the same answer: 36x^2 + 84xy^2 + 49y^4. Understanding both the FOIL method and the pattern for squaring binomials allows you to expand these expressions efficiently.