Expand using the Distributive Property: -6(5h - 3)

Answer 1

To expand the expression \(-6(5h - 3)\) using the Distributive Property, you multiply \(-6\) by each term inside the parentheses.

Starting with the expression:

\[ -6(5h - 3) \]

We distribute \(-6\) to both \(5h\) and \(-3\):

1. Multiply \(-6\) by \(5h\): \[ -6 \cdot 5h = -30h \]

2. Multiply \(-6\) by \(-3\): \[ -6 \cdot -3 = 18 \]

Now, combine the results:

\[ -30h + 18 \]

So, the expanded expression is:

\[ -30h + 18 \]

Answer 2

Factor the expression: 9x + 21(1 point)

Answer 3

To factor the expression \(9x + 21\), look for the greatest common factor (GCF) of the two terms.

In this case:

1. The GCF of \(9\) and \(21\) is \(3\).

Now, we can factor out \(3\):

\[ 9x + 21 = 3(3x + 7) \]

So, the factored expression is:

\[ 3(3x + 7) \]

Answer 4

Factor the expression: 35x + 20

Answer 5

To factor the expression \(35x + 20\), we first find the greatest common factor (GCF) of the two terms.

1. Identify the GCF:
   • The GCF of \(35\) and \(20\) is \(5\).

Now, we can factor out \(5\):

\[ 35x + 20 = 5(7x + 4) \]

So, the factored expression is:

\[ 5(7x + 4) \]

Answer 6

Add the expressions.(2.5x + 3) + (5x - 1.2)

Answer 7

To add the expressions \((2.5x + 3) + (5x - 1.2)\), we will combine like terms.

Start by rewriting the expression:

\[ 2.5x + 3 + 5x - 1.2 \]

Now, group the \(x\) terms and the constant terms:

1. Combine the \(x\) terms: \[ 2.5x + 5x = 7.5x \]

2. Combine the constant terms: \[ 3 - 1.2 = 1.8 \]

Putting it all together, we get:

\[ 7.5x + 1.8 \]

So, the result of the addition is:

\[ 7.5x + 1.8 \]

Answer 8

Subtract the expressions. (8y + 6) - (3y + 4)

Answer 9

To subtract the expressions \((8y + 6) - (3y + 4)\), first rewrite the expression by distributing the negative sign to both terms in the second parentheses:

\[ (8y + 6) - (3y + 4) = 8y + 6 - 3y - 4 \]

Now, combine like terms:

1. Combine the \(y\) terms: \[ 8y - 3y = 5y \]

2. Combine the constant terms: \[ 6 - 4 = 2 \]

Putting it all together, we have:

\[ 5y + 2 \]

So, the result of the subtraction is:

\[ 5y + 2 \]

Answer 10

Simplify the expression by using the Distributive Property and combining like terms. 5(3x + 4) - 7x - 3

Answer 11

To simplify the expression \(5(3x + 4) - 7x - 3\) using the Distributive Property and combining like terms, follow these steps:

1. Distribute \(5\) to the terms inside the parentheses: \[ 5(3x) + 5(4) = 15x + 20 \]

So, the expression becomes: \[ 15x + 20 - 7x - 3 \]

2. Combine like terms:
   • Combine the \(x\) terms: \[ 15x - 7x = 8x \]
   • Combine the constant terms: \[ 20 - 3 = 17 \]

Putting it all together, we get: \[ 8x + 17 \]

So, the simplified expression is: \[ 8x + 17 \]