Question

10 rewrite each expression by combining like terms. (a) part a $12ab - 7ab$ (b) part b $10x + 5y - 8x$

Explanation:

Part A

Step1: Identify like terms

Both terms \(12ab\) and \(7ab\) have the same variable part \(ab\), so they are like terms.

Step2: Combine coefficients

To combine like terms, we subtract the coefficients: \(12 - 7 = 5\), and keep the variable part \(ab\). So \(12ab - 7ab=(12 - 7)ab\)

Step3: Simplify the coefficient

\((12 - 7)ab = 5ab\)

Step1: Identify like terms

The terms \(10x\) and \(-8x\) have the same variable \(x\), so they are like terms. The term \(5y\) has a different variable \(y\), so it remains as is.

Step2: Combine coefficients of like terms

For the like terms \(10x\) and \(-8x\), we add their coefficients: \(10 - 8 = 2\), so \(10x-8x=(10 - 8)x\)

Step3: Rewrite the expression

Substitute the combined like terms back into the original expression: \((10 - 8)x+5y = 2x + 5y\)

Answer:

\(5ab\)

Part B