5 x 9 = (5 x 3) + (5 x 3) + (5 x 3)
9
Since 18 is a factor of 36, it is automatically the GCF of this problem.
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.)
To find the sum as a product of the greatest common factor of two numbers basically indicates that you need to use the distributive property. For example, 44+40=4(10+11). It's just how many times the GCF goes into the factors. In this case 4 goes into 40, 10 times and 4 goes into 44, 11 times.
(5 x 6) + (2 x 6) = 7 x 6 = 42
Yes.
The distributive property allows us to simplify expressions by distributing a term across a sum or difference. When factoring a polynomial, we can reverse this process by identifying common factors in each term of the polynomial. For example, in the expression ( ax + ay ), we can factor out ( a ) to get ( a(x + y) ). This reveals the common factor and simplifies the polynomial into a product of its factors.
Distributive.
10(2k + 5)
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)
(4 x 4) + (4 x 9) = 4 x 13 = 52
The GCF is 18. The Distributive property states that 36 x (50 + 4) = (36 x 50) + (36 x 4)
The Distributive Property
112
The distributive property states that a(b + c) = ab + ac. In the case of 16 plus 48, we can factor out a common factor, like 16, to simplify the addition: 16 + 48 can be expressed as 16(1 + 3) since 48 is 16 times 3. This shows how the distributive property can help break down and simplify calculations involving addition.