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anemone
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If $p+q+r+s+t+u=0$ and $p^3+q^3+r^3+s^3+t^3+u^3=0$, prove that
$(p+r)(p+s)(p+t)(p+u)=(q+r)(q+s)(q+t)(q+u)$.
$(p+r)(p+s)(p+t)(p+u)=(q+r)(q+s)(q+t)(q+u)$.
[sp]anemone said:If $p+q+r+s+t+u=0$ and $p^3+q^3+r^3+s^3+t^3+u^3=0$, prove that
$(p+r)(p+s)(p+t)(p+u)=(q+r)(q+s)(q+t)(q+u)$.
The equation is a mathematical expression that represents the multiplication of four terms, (p+r), (p+s), (p+t), and (p+u). The result of this multiplication is equal to the multiplication of four other terms, (q+r), (q+s), (q+t), and (q+u).
This equation is significant because it demonstrates the distributive property of multiplication, which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. It is also a common algebraic expression that is used in various mathematical calculations and proofs.
For example, if we let p=2, r=3, s=4, t=5, and u=6, then we have (2+3)(2+4)(2+5)(2+6) = (3+3)(3+4)(3+5)(3+6), which simplifies to 120 = 120. This shows that the equation holds true for these specific values, and it can be generalized to any other values of p, r, s, t, and u.
This equation can be used in various real-life situations that involve multiplication or distribution of quantities. For example, it can be used in business and finance to calculate the total cost or revenue of a product or service that is sold in different quantities and prices. It can also be used in physics and engineering to calculate the total force or energy of a system that is composed of multiple components.
If this equation is not true, it would mean that the distributive property of multiplication is not valid, which could lead to errors in mathematical calculations and proofs. It would also indicate a flaw in the understanding of basic algebraic concepts. However, this equation has been proven to be true, and it is a fundamental principle in mathematics.