Question

stage 2: simplifying expressions (medium)
simplify each expression.
1 3x + 5x
2 7y - 2y
3 4(a + 6)
4 2x + 3 + x
5 5(b - 2)

Explanation:

Problem 1: \( 3x + 5x \)

Step 1: Combine like terms

Since \( 3x \) and \( 5x \) are like terms (they have the same variable \( x \) with the same exponent), we can add their coefficients. The coefficient of \( 3x \) is 3 and the coefficient of \( 5x \) is 5. So we calculate \( 3 + 5 \).
\( 3x + 5x=(3 + 5)x \)

Step 2: Calculate the sum of coefficients

\( 3+5 = 8 \), so \( (3 + 5)x=8x \)

Step 1: Combine like terms

\( 7y \) and \( 2y \) are like terms (same variable \( y \) with the same exponent). We subtract their coefficients. The coefficient of \( 7y \) is 7 and the coefficient of \( 2y \) is 2. So we calculate \( 7-2 \).
\( 7y - 2y=(7 - 2)y \)

Step 2: Calculate the difference of coefficients

\( 7 - 2=5 \), so \( (7 - 2)y = 5y \)

Step 1: Apply the distributive property

The distributive property states that \( c(a + b)=ca+cb \), where \( c = 4 \), \( a=a \) and \( b = 6 \). So we multiply 4 with each term inside the parentheses.
\( 4(a + 6)=4\times a+4\times6 \)

Step 2: Perform the multiplications

\( 4\times a = 4a \) and \( 4\times6=24 \), so \( 4\times a+4\times6 = 4a + 24 \)

Answer:

\( 8x \)

Problem 2: \( 7y-2y \)