The distributive property is a property for multiplying with parentheses. It states that a(b+c)=ab+ac. The means that 3(x+2)=3x+6, for example. Basically, the distributive property says you must multiply everything within the parentheses by the number outside the parentheses.
The distributive property.
Distributive Property
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.)
Its quiet simple. All you have to know is that when you use the distributive property in math, it's most likely and equation. So you basically remove the parentheses. AKA(expanding the equation)
The distributive property is a property for multiplying with parentheses. It states that a(b+c)=ab+ac. The means that 3(x+2)=3x+6, for example. Basically, the distributive property says you must multiply everything within the parentheses by the number outside the parentheses.
The distributive property.
The process of multiplying a number outside a set of parentheses to everything inside the parentheses is called distributing or the distributive property. This property is used to simplify algebraic expressions by multiplying the external number to each term inside the parentheses.
To apply the distributive property to an algebraic expression, you multiply each term inside the parentheses by the number or variable outside the parentheses. For example, to simplify 2(x + 3), you would multiply 2 by both x and 3, resulting in 2x + 6.
Distributive Property
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.)
Its quiet simple. All you have to know is that when you use the distributive property in math, it's most likely and equation. So you basically remove the parentheses. AKA(expanding the equation)
Adding parentheses in an equation can change the order of operations and is known as the distributive property. This property allows you to group terms together for simplifying expressions or equations.
Here is how to multiply using the distributive property:First, the equation: 9 (x + 3) = 35There must be parentheses for the distributive property, and a number outside those parentheses. The next step is to multiply 9 by x and 9 by 3 individually, and put an addition symbol in the middle.The second equation: 9x + 27 = 35Then, subtract 27: 9x = 18Divide by 9 on both sides: x = 2.That is how you multiply using the distributive property.
To be picky, the distributive property is about multiplication, but division is defined in terms of multiplication, so your question can be answered!Say you have (6xy+15y)/(3y). The distributive property will say this is equal to 6xy/3y + 15y/3y = 2x + 5.Notice that the "/3y" has been distributed onto each term inside the parentheses.
The information in parentheses could mean you do that section first, (PEMDAS) , or it could have two parentheses to make the equivalent of a multiplication problem, such as (2)(3), or (2 + 3)(2 + 3) , which in that case you must use the distributive property.
Wrong! See below. No, you cannot use the distributive property for subtraction. Let's say that your expression is: (5 + 4) - 3 We know that parentheses must be handled first, so we know that the correct answer is: (5 + 4) - 3 = 9 - 3 = 6. But let's say that you tried to use the distributive propertyand applied "- 3" to each term in the parentheses. You would get: (5 + 4) - 3 = (5 - 3) + (4 - 3) = 3 In fact, you would have subtracted not 3, but 6! * * * * * All very true except that this is the associative property - not distributive The distributive property, which IS valid, gives a*(b - c) = a*b - a*c