(8x^4+1)^2=

Jasonbradley

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Jun 16, 2024

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Expanding (8x^4 + 1)^2

This expression represents the square of a binomial, which can be expanded using the FOIL method or by recognizing the square of a sum pattern.

Using FOIL

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials by systematically combining all the terms:

1. First: Multiply the first terms of each binomial: (8x^4) * (8x^4) = 64x^8
2. Outer: Multiply the outer terms of the binomials: (8x^4) * (1) = 8x^4
3. Inner: Multiply the inner terms of the binomials: (1) * (8x^4) = 8x^4
4. Last: Multiply the last terms of each binomial: (1) * (1) = 1

Now, add all the results together:

64x^8 + 8x^4 + 8x^4 + 1

Finally, combine the like terms:

64x^8 + 16x^4 + 1

Using the Square of a Sum Pattern

The square of a sum pattern states: (a + b)^2 = a^2 + 2ab + b^2

In our case, a = 8x^4 and b = 1. Applying the pattern:

(8x^4 + 1)^2 = (8x^4)^2 + 2(8x^4)(1) + (1)^2

Simplifying:

64x^8 + 16x^4 + 1

Therefore, both methods lead to the same result: (8x^4 + 1)^2 = 64x^8 + 16x^4 + 1.