The distributive property states: a(b+c)=a•b+a•c. In other words, the terms inside the parentheses are multiplied by the factor outside the parentheses; remember that a(b)=a•b
1.) 4x+12
2.) -28+7y
3.) 18x+30y-24
4.) For number 4, is the question 9(a-3/3) or a different expression? If it’s the first one, then it equals 9a-9.
5.) To factor out the GCF, we need to find the greatest factor that divides into both 64 and 24. We will find that 8 is the largest factor of 24 and 64. Therefore, all terms are divided by 8, and 8 remains out in front. We are essentially “undoing” distribution. We need to factor out a number that will make the multiples of 64 and 24.
(64+24)/8
5.) Answer: 8(8x+3)
Notice that if we distribute, we end up with 64x+24, so we simply revers distribution. Since distribution is multiplication, and division reverse multiplication into a simplified form, we divided each term by the GCF of 8.
6.) Factor out a GCF that divides into -5y and -35. The GCF is 5, since 5 divides evenly into both terms.
(-5y-35)/5
5(-y-7) is the answer.
Also notice that even though both terms were divided by 5, we kept the 5 out in front to distribute. This is because the goal of factoring is to break the expression down into a simplified, equivalent form.