QUESTION 1: Using distribution and combining like terms to simplify: 3(y + 5) - 6y
EXPLANATION
3(y +
5) - 6y = 3y + 15 – 6y Using
the distributive property to remove parentheses
= 3y +
15 + (- 6y) Writing
subtraction as addition of a negative
= 3y +
(- 6y) +15 Using the
commutative property to rearrange terms
= - 3y
+ 15 Combining like terms
ANSWER: -3y + 15
QUESTION 2: Use the distributive property to remove the parentheses (-2 + 4x + 4v) (-7)
EXPLANATION: We use the
distributive property as follows
(-2 +
4x + 4v) (-7) = (-2)(-7) + (4x)(-7) + (4v)(-7)
= 14 +
(-28x) + (-28v)
= 14 -
28x – 28v
ANSWER: 14 - 28x – 28v
QUESTION 3: Subtract -2/3 – 5/7 Write your answer in simplest form
EXPLANATION: The least common denominator of -2/3 and -5/7
is 21
So we write each fraction with a denominator of 21, then
subtract.
-2/3 – 5/7 = - 2(7)/3(7) – 5(3)/7(3)
= -14/21 – 15/21
= (-14-15)/21
= -29/21
ANSWER: -29/21
QUESTION 4: Multiply -1/7 * (-5/3) Write your answer in simplest form
EXPLANATION: We can work as follows
-1/7 * (-5/3) = 5/21 Multiplying
the numerators/ Multiplying the denominators
Note that the answer is positive because we're multiplying
two negative numbers
ANSWER: 5/21
QUESTION 5: Evaluate the expression when b = -5
b^2 + 5b +4
EXPLANATION: We substitute -5 for b, then we simplify by
following the order of operations.
b^2 + 5b +4 = (-5)^2 + 5(-5) + 4 Evaluating the exponent
= 25 - 25 + 4 Multiplying
= 4 Adding and
subtracting from left to right
ANSWER: 4
QUESTION 6: Simplify (3y)^4 Write your answer without parentheses.
Method 1: By definition, the exponent 4 tells us how many
times 3y appears in the product.
We can multiply to get the following:
(3y)^4 = 3y * 3y * 3y * 3y
= 3 * 3 * 3 * 3 * y * y * y * y
= 81(y^4)
Note that the exponent 4 in (3y)^4 applies to both the 3 and
the y
Method 2: The method above suggests a rule called the power
of a product rule of exponents.
It says that for any integer n, and any numbers a
and b, we have the following:
(ab)^n = a^n b^n
Using the rule with the current problem, we get the
following:
(3y)^4 = 81(y^4)
ANSWER: 81y^4
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