Simplify 5 (7r - 2) - 14r + 4.
To simplify this expression, we will use the distributive property.
First, we distribute the 5 to the terms inside the parentheses:
5 * 7r = 35r
5 * -2 = -10
So the expression becomes: 35r - 10 - 14r + 4.
Next, we combine like terms:
35r - 14r = 21r
-10 + 4 = -6
So the simplified expression is: 21r - 6.
simplify 17d - 33 + 9 (2d + 6) - 11
To simplify this expression, we will continue using the distributive property.
First, we distribute the 9 to the terms inside the parentheses:
9 * 2d = 18d
9 * 6 = 54
So the expression becomes: 17d - 33 + 18d + 54 - 11.
Next, we combine like terms:
17d + 18d = 35d
-33 + 54 - 11 = 10
So the simplified expression is: 35d + 10.
Simplify 6 (3q - 4) + 18 - 12q - 7 (4q + 5)
To simplify this expression, we will continue using the distributive property.
First, we distribute the 6 to the terms inside the parentheses:
6 * 3q = 18q
6 * -4 = -24
So the expression becomes: 18q - 24 + 18 - 12q - 7(4q + 5).
Next, we distribute the -7 to the terms inside the parentheses:
-7 * 4q = -28q
-7 * 5 = -35
So the expression becomes: 18q - 24 + 18 - 12q - 28q - 35.
Next, we combine like terms:
18q - 12q - 28q = -22q
-24 + 18 + (-35) = -41
So the simplified expression is: -22q - 41.
simplify -5 + 3/4(8h + 12) - 10h
To simplify this expression, we will continue using the distributive property.
First, we distribute the 3/4 to the terms inside the parentheses:
(3/4) * 8h = 6h
(3/4) * 12 = 9
So the expression becomes: -5 + 6h + 9 - 10h.
Next, we combine like terms:
6h - 10h = -4h
-5 + 9 = 4
So the simplified expression is: -4h + 4.
Factor 24n - 32 using GCF
To factor 24n - 32 using the greatest common factor (GCF), we will find the GCF of the two terms.
The prime factorization of 24 is 2 * 2 * 2 * 3, and the prime factorization of 32 is 2 * 2 * 2 * 2 * 2.
The common factors between 24 and 32 are 2 * 2 * 2, which is equal to 8.
Now, we can factor out the GCF from both terms:
24n - 32 = 8(3n - 4)
Therefore, 24n - 32 can be factored as 8(3n - 4) using the greatest common factor.