If we multiply "a" and "b",when will:
a. the product be larger than both "a" and "b"?
b. the Product be less than "a"?
c. the product be less than "b"?
d. the product be less than"a" and "b"?
e. the product be greater than "a"?
f. the product be greater than "b"?
g. the product be greater than "a" and "b"?
h. the product be equal to either "a" and "b"?
i. the product be zero?
I suppose what you mean by "If we multiply "a" and "b..." is the product ab of a and b.
a) We want a<ab and b<ab
Consider when they have the same sign or different signs. If a and b are pos., then both a>1 and b>1
If both are neg., then a<ab and b<ab hold for all a,b negative.
If they have different signs then
a<ab or b<ab will not hold for one of them because ab<0 but one is greater than 0. Therefore the empty set with different signs.
All of the rest are along the same lines, except i). They can both be 0, but at least one of a,b must be 0.
Show some work so we can see where the difficulties are. I don't see how it helps if I do all of them. There are a lot of cases to consider, so you need to check your work carefully.
bot you there?
Yes, I'm here. Did you have any further questions about the multiplication of "a" and "b"?
whats the product of (3x + 4) (x-2)
To find the product of (3x + 4) and (x-2), we can use the distributive property of multiplication.
(3x + 4) (x-2) = 3x(x-2) + 4(x-2)
Simplifying the expression, we get:
= 3x^2 - 6x + 4x - 8
= 3x^2 - 2x - 8
Therefore, the product of (3x + 4) and (x-2) is 3x^2 - 2x - 8.
what's the product of (2y-1) (4y - 3)
To find the product of (2y-1) and (4y-3), we can use the distributive property of multiplication.
(2y-1)(4y-3) = 2y(4y) - 2y(3) - 1(4y) + 1(3)
Simplifying, we get:
= 8y^2 - 6y - 4y + 3
= 8y^2 - 10y + 3
Therefore, the product of (2y-1) and (4y-3) is 8y^2 - 10y + 3.
To answer each of the questions, we need to consider the relationship between the values of a, b, and their product ab. Let's go through each case one by one:
a) The product ab will be larger than both a and b when both a and b are positive numbers. In this case, when a > 0 and b > 0.
b) The product ab will be less than a when b is between 0 and 1, exclusive. In other words, if 0 < b < 1.
c) The product ab will be less than b when a is between 0 and 1, exclusive. In other words, if 0 < a < 1.
d) The product ab will be less than both a and b when either a or b is a negative number. In other words, if either a < 0 or b < 0.
e) The product ab will be greater than a when b is larger than 1. In other words, if b > 1.
f) The product ab will be greater than b when a is larger than 1. In other words, if a > 1.
g) The product ab will be greater than both a and b when both a and b are larger than 1. In this case, when a > 1 and b > 1.
h) The product ab will be equal to either a or b when one of them is 0. In this case, if either a = 0 or b = 0.
i) The product ab will be zero if either a = 0 or b = 0. In other words, if at least one of the variables is 0.
Remember, these relationships hold true for real numbers. It's important to consider all possible scenarios and take note of any specific conditions mentioned for each case.