(3−8w2)2

Jasonbradley

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Jun 16, 2024

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Expanding (3−8w2)2

The expression (3−8w2)2 represents the square of a binomial. To expand it, we can use the FOIL method or the square of a binomial pattern.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us to multiply each term in the first binomial with each term in the second binomial:

1. First: Multiply the first terms of each binomial: 3 * 3 = 9
2. Outer: Multiply the outer terms of the binomials: 3 * -8w2 = -24w2
3. Inner: Multiply the inner terms of the binomials: -8w2 * 3 = -24w2
4. Last: Multiply the last terms of the binomials: -8w2 * -8w2 = 64w4

Adding all these terms together, we get:

9 - 24w2 - 24w2 + 64w4

Combining like terms, we obtain the final expanded form:

64w4 - 48w2 + 9

Using the Square of a Binomial Pattern

The square of a binomial pattern states:

(a - b)2 = a2 - 2ab + b2

In this case, a = 3 and b = 8w2. Applying the pattern, we get:

32 - 2(3)(8w2) + (8w2)2

Simplifying, we arrive at the same expanded form:

64w4 - 48w2 + 9

Therefore, both methods lead to the same result: (3−8w2)2 = 64w4 - 48w2 + 9.