Expand the following algebraic expressions: 1. 6(x+3) 2. −4(x+3) 3. x(x+2) 4. 20I(a+3b) + 4(2a+b) 5. 4(2b+1)…

Question

Expand the following algebraic expressions: 1. 6(x+3) 2. −4(x+3) 3. x(x+2) 4. 20I(a+3b) + 4(2a+b) 5. 4(2b+1) − 3(6-2)

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the expressions:

1.

Distribute the 6 to each term inside the parenthesis.
$6(x+3) = 6 \cdot x + 6 \cdot 3$
Perform the multiplications.
$6x + 18$
The expanded expression is:
$\boxed{\text{6x + 18}}$
2.
Distribute the $-4$ to each term inside the parenthesis.
$-4(x+3) = -4 \cdot x + (-4) \cdot 3$
Perform the multiplications.
$-4x - 12$
The expanded expression is:
$\boxed{\text{-4x - 12}}$
3.
Distribute the $x$ to each term inside the parenthesis.
$x(x+2) = x \cdot x + x \cdot 2$
Perform the multiplications.
$x^2 + 2x$
The expanded expression is:
\boxed{\text{x^2 + 2x}}
4.
Distribute $20I$ into the first parenthesis and 4 into the second parenthesis.
$20I(a+3b) + 4(2a+b) = (20I \cdot a + 20I \cdot 3b) + (4 \cdot 2a + 4 \cdot b)$
Perform the multiplications.
$20Ia + 60Ib + 8a + 4b$
The expanded expression is:
$\boxed{\text{20Ia + 60Ib + 8a + 4b}}$
5.
Distribute 4 into the first parenthesis and simplify the second parenthesis.
$4(2b+1) - 3(6-2) = (4 \cdot 2b + 4 \cdot 1) - 3(4)$
Perform the multiplications.
$8b + 4 - 12$
Combine the constant terms.
$8b - 8$
The expanded expression is:
$\boxed{\text{8b - 8}}$

Expand the following algebraic expressions: 1. 6(x+3) 2. -4(x+3) 3. x(x+2) 4. 20I(a+3b) + 4(2a+b) 5. 4(2b+1) - 3(6-2)