Question

expand the expressions and simplify.
$5(x + 4) + 3(x + 2) = \boxed{8x + 26}$
$4(x + 3) + 2(x - 4) = \boxed{\quad}$
$4(x + 2) + 2(x + 5) = \boxed{\quad}$
options: $6x + 18$, $8x + 4$, $6x + 4$, $7x - 18$

Explanation:

First Sub - Question: \(4(x + 3)+2(x - 4)\)

Step 1: Expand the brackets

Using the distributive property \(a(b + c)=ab+ac\), we have:
\(4(x + 3)=4x+12\) and \(2(x - 4)=2x-8\)
So the expression becomes \(4x + 12+2x-8\)

Step 2: Combine like terms

Combine the \(x\) - terms and the constant terms separately.
For the \(x\) - terms: \(4x+2x = 6x\)
For the constant terms: \(12-8 = 4\)
So the simplified expression is \(6x + 4\)

Second Sub - Question: \(4(x + 2)+2(x + 5)\)

Step 1: Expand the brackets

Using the distributive property \(a(b + c)=ab+ac\), we get:
\(4(x + 2)=4x+8\) and \(2(x + 5)=2x + 10\)
The expression then is \(4x+8+2x + 10\)

Step 2: Combine like terms

Combine the \(x\) - terms: \(4x+2x=6x\)
Combine the constant terms: \(8 + 10=18\)
So the simplified expression is \(6x+18\)

Answer:

For \(4(x + 3)+2(x - 4)\): \(6x + 4\)
For \(4(x + 2)+2(x + 5)\): \(6x + 18\)