Determine the GCF (greatest common factor) for the expression 18j+27

Question

.(1 point)
The GCF of 18j+27
is
.

Answer 1

To find the greatest common factor (GCF) of the expression \(18j + 27\), we need to determine the GCF of the coefficients \(18\) and \(27\).

1. Factor the coefficients:

   • The factors of \(18\) are \(1, 2, 3, 6, 9, 18\).
   • The factors of \(27\) are \(1, 3, 9, 27\).

2. Identify the common factors:

   • The common factors of \(18\) and \(27\) are \(1, 3, 9\).

3. The greatest common factor among these is \(9\).

Thus, the GCF of \(18j + 27\) is \(\boxed{9}\).

Answer 2

Determine the GCF (greatest common factor) of the expression 42m−28n
.(1 point)
The GCF for 42m−28n
is

Answer 3

To find the greatest common factor (GCF) of the expression \(42m - 28n\), we need to determine the GCF of the coefficients \(42\) and \(28\).

1. Factor the coefficients:

   • The factors of \(42\) are \(1, 2, 3, 6, 7, 14, 21, 42\).
   • The factors of \(28\) are \(1, 2, 4, 7, 14, 28\).

2. Identify the common factors:

   • The common factors of \(42\) and \(28\) are \(1, 2, 7, 14\).

3. Determine the greatest common factor:

   • The greatest common factor among these is \(14\).

Thus, the GCF of \(42m - 28n\) is \(\boxed{14}\).

Answer 4

Use properties of operations to factor 8w+16
using GCF.(1 point)
Responses

6(2w+10)
6 times open paren 2 w plus 10 close paren

4(2w+4)
4 times open paren 2 w plus 4 close paren

2(4w+8)
2 times open paren 4 w plus 8 close paren

8(w+2)

Answer 5

To factor \(8w + 16\) using the greatest common factor (GCF), we first determine the GCF of the terms \(8w\) and \(16\).

1. The coefficients are \(8\) and \(16\).
2. The GCF of \(8\) and \(16\) is \(8\).

Now we can factor \(8\) out of the expression:

\[ 8w + 16 = 8(w + 2) \]

So, the correct answer is:

\(\boxed{8(w + 2)}\)

Answer 6

Factor −27h+6
using the GCF.(1 point)
Responses

3(−9h+2)
3 times open paren negative 9 h plus 2 close paren

3(−9h−2)
3 times open paren negative 9 h minus 2 close paren

3(9h+2)
3 times open paren 9 h plus 2 close paren

3(−9h−2)

Answer 7

To factor the expression \( -27h + 6 \) using the greatest common factor (GCF), we first identify the GCF of the coefficients \(-27\) and \(6\).

1. The GCF of \( -27 \) and \( 6 \) is \( 3 \) (the absolute values) since \(3\) divides both numbers.

Now, we factor out \(3\) from the expression:

\[ -27h + 6 = 3(-9h + 2) \]

So the correct answer is:

\(\boxed{3(-9h + 2)}\)

Answer 8

Use the distributive property to expand the following expression:

−5(−3−11g)
(1 point)
Responses

55g−15
55 g minus 15

−55g+15
negative 55 g plus 15

55g+15
55 g plus 15

−55g−15

Answer 9

To expand the expression \(-5(-3 - 11g)\) using the distributive property, we distribute \(-5\) to each term inside the parentheses:

\[ -5(-3) + (-5)(-11g) \]

Calculating each part:

\[ -5(-3) = 15 \] \[ -5(-11g) = 55g \]

Now, combine the results:

\[ 15 + 55g \]

This can also be written as:

\[ 55g + 15 \]

Thus, the correct answer is:

\(\boxed{55g + 15}\)

Answer 10

Simplify the expression by combining like terms.

28x+310y−58x+410y
(1 point)
Responses

1418xy
14 over 18 x y

−38x+710y
negative 3 eighths x plus 7 tenths y

418xy
4 over 18 x y

710x+78y

Answer 11

To simplify the expression \(28x + 310y - 58x + 410y\), we need to combine the like terms (terms with \(x\) and \(y\) respectively).

1. Combine the \(x\) terms: \[ 28x - 58x = -30x \]

2. Combine the \(y\) terms: \[ 310y + 410y = 720y \]

Now, we combine the results: \[ -30x + 720y \]

So the simplified expression is: \(\boxed{-30x + 720y}\)

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