Get expert advice and community support for all your questions on IDNLearn.com. Our experts are ready to provide prompt and detailed answers to any questions you may have.

Simplify the expression:

[tex]\[8(3a + 2)(5a - 3)\][/tex]


Sagot :

Certainly! Let's expand the expression [tex]\(8(3a + 2)(5a - 3)\)[/tex] step by step.

### Step 1: Distribute the 8

First, keep the 8 outside for now and focus on expanding the binomials inside the parentheses.

[tex]\[ 8(3a + 2)(5a - 3) \][/tex]

### Step 2: Expand the binomials using the distributive property (FOIL method)

To expand [tex]\((3a + 2)(5a - 3)\)[/tex], we use the FOIL method which stands for:

- First terms
- Outer terms
- Inner terms
- Last terms

Let's identify each component:

#### First terms:
[tex]\[ (3a) \times (5a) = 15a^2 \][/tex]

#### Outer terms:
[tex]\[ (3a) \times (-3) = -9a \][/tex]

#### Inner terms:
[tex]\[ (2) \times (5a) = 10a \][/tex]

#### Last terms:
[tex]\[ (2) \times (-3) = -6 \][/tex]

Now, combine the like terms (middle terms: outer and inner):
[tex]\[ -9a + 10a = 1a \][/tex]

So, the expanded form of [tex]\((3a + 2)(5a - 3)\)[/tex] is:
[tex]\[ 15a^2 + 1a - 6 \][/tex]

### Step 3: Distribute the 8 to each term inside the parentheses

Now, multiply each term in the expanded polynomial by 8:
[tex]\[ 8 \times 15a^2 = 120a^2 \][/tex]
[tex]\[ 8 \times 1a = 8a \][/tex]
[tex]\[ 8 \times -6 = -48 \][/tex]

### Step 4: Combine all the terms

Putting it all together, we get the expanded polynomial:
[tex]\[ 120a^2 + 8a - 48 \][/tex]

So, the fully expanded form of [tex]\(8(3a + 2)(5a - 3)\)[/tex] is:
[tex]\[ 120a^2 + 8a - 48 \][/tex]