Question

practice 2 expanding and factoring algebraic expressions
expand each expression.

1. 2(8x + 16)
2. 4(12 + 3p)
3. 5(14k - 10)
4. 3(8a - 24)

Explanation:

Problem 1: Expand \( 2(8x + 16) \)

Step 1: Apply the distributive property

The distributive property states that \( a(b + c) = ab + ac \). Here, \( a = 2 \), \( b = 8x \), and \( c = 16 \). So we multiply 2 by each term inside the parentheses.
\( 2\times8x + 2\times16 \)

Step 2: Simplify the products

Calculate \( 2\times8x = 16x \) and \( 2\times16 = 32 \).
\( 16x + 32 \)

Step 1: Apply the distributive property

Using \( a(b + c) = ab + ac \) with \( a = 4 \), \( b = 12 \), and \( c = 3p \).
\( 4\times12 + 4\times3p \)

Step 2: Simplify the products

\( 4\times12 = 48 \) and \( 4\times3p = 12p \).
\( 48 + 12p \) (or \( 12p + 48 \))

Step 1: Apply the distributive property

For \( a(b - c) = ab - ac \), here \( a = 5 \), \( b = 14k \), \( c = 10 \).
\( 5\times14k - 5\times10 \)

Step 2: Simplify the products

\( 5\times14k = 70k \) and \( 5\times10 = 50 \).
\( 70k - 50 \)

Answer:

\( 16x + 32 \)

Problem 2: Expand \( 4(12 + 3p) \)