81 a² - 25
is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)
Step-by-step explanation:
The difference of two squares is a binomial of two terms each term is a square and the sign between the two terms is (-), its factorization is the product of two identical binomials with different middle signs
- a² - b² is a difference of two squares
- a² - b² = (a + b)(a - b)
∵ The binomial is 81 a² - 25
∵
= 9
∵
= a
∴ 
∵
= 5
∵
= z³
∴ 
- The two terms have square root
∵ The sign between them is (-)
∴ 81 a² - 25
is a difference of two squares
∵ Its factorization is two identical brackets with different
middle signs
∵ 81 a² = 9a × 9a
∵ 25
= 5z³ × 5z³
- The terms of the two brackets are 9a and 5z³
∴ 81 a² - 25
= (9a + 5z³)(9a - 5z³)
81 a² - 25
is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)
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Answer:

Step-by-step explanation:
Given
per person
Required
Represent as an equation
For 1 person, the admission fee is 2
For p people, the admission fee will be 2p.
Hence:

1.Identify the fractions. Using the distributive property, you’ll eventually turn them into integers.
2.For all fractions, find the lowest common multiple (LCM) -- the smallest number that both denominators can fit neatly into. This will allow you to add fractions.
3.Multiply every term in the equation by the LCM.
4.Isolate variables adding or subtracting like terms on both sides of the equals sign.
5.Combine like terms.
6.Solve the equation and simplify, if needed.
Cutting her time by 50% means reducing her time by half. Half of 45 seconds is 22.5 seconds. Therefore, to make the team, she must run a lap in 22.5 seconds.