Question

Ali factored the expression 20x + 10 and got 2(10x + 5)When she checked it using the distributive property, she got the original problem. Since her check worked, she thinks she has the correct answer. How can that be? Explain her mistake.

Answer 1

Ali's initial factoring of the expression 20x + 10 was incorrect because she did not factor out the greatest common factor. The correct factoring is 10(2x + 1), which provides the simplest form when applying the distributive property: 10*2x + 10*1 = 20x + 10.

Step-by-step explanation:

The student made a mistake in factoring the expression 20x + 10. Ali's factored form, 2(10x + 5), is not completely factored because it does not represent the greatest common factor (GCF) of the original terms. The correct factorization involves factoring out the GCF, which in this case is 10, since both 20x and 10 are divisible by 10. The proper factorization is 10(2x + 1), which simplifies the expression while maintaining the same value when the distributive property is applied.

When using the distributive property to check the factoring, we would take 10 and distribute it across the terms in the parentheses to get: 10*2x + 10*1 = 20x + 10, proving that the factorization is correct. The confusion may arise from the fact that the original check by Ali still resulted in the initial expression, but it's important to factor out the greatest common factor to achieve the simplest form.