What is the completely factored form of p4 – 16?
Asked by wiki @ in Mathematics viewed by 501 People
Answered by wiki @
Answer:
(p+2)(p-2)(p²+4)
Step-by-step explanation:
The binomial p⁴-16 is a difference of squares. This is because p⁴ is a perfect square, as is 16. This means we can write it as the sum of the square roots multiplied by the difference of the square roots:
(p²+4)(p²-4)
The first binomial, p²+4, cannot be factored any further.
The second binomial, p²-4, is another difference of squares, since p² is a perfect square, as is 4:
(p+2)(p-2)
This gives us
(p²+4)(p+2)(p-2)
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