Question

equivalent to the given expression. 21. 24x + 20y

Explanation:

Step1: Find GCF of 24 and 20

The greatest common factor (GCF) of 24 and 20 is 4, since factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and factors of 20 are 1, 2, 4, 5, 10, 20. The largest common one is 4.

Step2: Factor out GCF

Using the distributive property \(ab + ac = a(b + c)\), we factor out 4 from \(24x + 20y\).
\(24x\div4 = 6x\) and \(20y\div4 = 5y\), so \(24x + 20y = 4(6x + 5y)\).
We can also have other equivalent forms by factoring out other common factors (like 2):

Step3: Factor out 2

\(24x\div2 = 12x\) and \(20y\div2 = 10y\), so \(24x + 20y = 2(12x + 10y)\).
Or we can rewrite the terms:

Step4: Rewrite terms (e.g., split coefficients)

\(24x + 20y = 12x + 12x + 10y + 10y\) (though this is less concise than factoring). Another factoring with GCF 4 is the most standard equivalent form.

Answer:

\(4(6x + 5y)\) (or other equivalent forms like \(2(12x + 10y)\) etc.)