Question

Angelina factored (x - 4^8 ) and wrote that it was equal to (x^2 - 4^2)^2(x^2 + 4^2). Use complete sentences to explain how you could confirm whether Angela’s solution is correct. Prove your conclusion by multiplying out Angela’s solution.

Answer 1

Given is (x - 4⁸)

Her factors are (x² - 4²)² (x² + 4²)

Let us prove whether her solution is correct or not.

(x² - 4²)² (x² + 4²)
(x⁴ - 4⁴) (x² + 4²) ; Follow PEMDAS rule as well as exponential multiplication rule which tells that when exponents are multiplied, the exponents will be added.

By using FOIL(First, Outside, Inside, Last) Method, we can prove if Angelina's solution is correct. NOTE: Do not disregard the positive or negative.

(x⁴ - 4⁴) (x² + 4²) ; For the First, multiply the first terms. They are underlined.
This gives you a partial answer: x⁶ (Exponential Law of Multiplication is applied)

(x⁴ - 4⁴) (x² + 4²) ; For the Outside, multiply the outside terms. They are underlined. This gives you an additional to the partial answer: x⁶ + 4²x⁴

(x⁴ - 4⁴) (x² + 4²) ; For the Inside, multiply the inside terms. They are underlined. This gives you an additional to the partial answer: x⁶ + 4²x⁴ - 4⁴x²

(x⁴ - 4⁴) (x² + 4²) ; For the Last, multiply the last terms. They are underlined. This will give you an additional to the final answer: x⁶ + 4²x⁴ - 4⁴x² - 16⁶ = 0

Final Answer in complete sentence:
The result of multiplying the factors is x⁶ + 4²x⁴ - 4⁴x² - 16⁶ = 0 and is too far compared to (x - 4⁸) which is already a factor.