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Q: Can you use the distributive property to help you expand and factor expressions?

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10(2k + 5)

(3 x 12) + (4 x 12) = 7 x 12 = 84

3(3 + 5)

Distributive.

The GCF is 6.

The GCF is 16.

12a4 + 16a64a4(3 + 4a2)=========

The GCF of 24 and 30 is 6. The distributive property states that 24 x 30 = (20 x 30) + (4 x 30)

Suppose x and y are two terms with GCF k where the assumption (in this context) is that k is greater than 1. That implies that x = pk and y = qk where p and q are coprime terms. Then x + y = pk + qk and, using the distributive property, this is k*(p + q).

The Distributive Property

112

The GCF of 24 and 64 is 8. You use the distributive property to show another way to write the sum. 8(3 + 8)

You need at least two numbers to find a GCF.

9

The GCF is 18. The Distributive property states that 36 x (50 + 4) = (36 x 50) + (36 x 4)

It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question! It does not matter whether you use the distributive or any other property; something that does not exist cannot be found!

You look for a common factor between the two terms, take it out, and use the distributive property.

Since 18 is a factor of 36, it is automatically the GCF of this problem.

It's not necessary. Since 12 is a factor of 72, it is automatically the GCF.

That's 60rs + 24s, which factors to 12s(5r + 2)

An unnecessary one. 42 + 96 = 138

A property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses.

The least common factor of any two expressions is 1.

Distributive PropertyThe Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, that 2(3 + 4) = 2×3 + 2×4. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses (or factor something out); any time a computation depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the Distributive Property.Why is the following true? 2(x + y) = 2x + 2ySince they distributed through the parentheses, this is true by the Distributive Property.Use the Distributive Property to rearrange: 4x - 8The Distributive Property either takes something through a parentheses or else factors something out. Since there aren't any parentheses to go into, you must need to factor out of. Then the answer is "By the Distributive Property, 4x - 8 = 4(x - 2)""But wait!" you say. "The Distributive Property says multiplication distributes over addition, not subtraction! What gives?" You make a good point. This is one of those times when it's best to be flexible. You can either view the contents of the parentheses as the subtraction of a positive number ("x - 2") or else as the addition of a negative number ("x + (-2)"). In the latter case, it's easy to see that the Distributive Property applies, because you're still adding; you're just adding a negative.The other two properties come in two versions each: one for addition and the other for multiplication. (Note that the Distributive Property refers to both addition and multiplication, too, but to both within just one rule.)

The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. YOu have only one term "8 + W" in the question so there cannot be a GCF. It is not possible to find any factor (other than 1 and 8 + W, itself, without further information about W.The distributive property has no relevance to this question.