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distributive property

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1. Could you share a few specific mathematical examples to demonstrate For instance, if I said an important concept of distributive property for the following example is?

Example

4(x+2) = 4x + 8

2. When we square a product, we square each factor in the product. For example (4b) 2= 16b2. Explain why we cannot square a sum by simply squaring each term of the sum. For example, (a + b) 2 is not equal to a2 + b2. Please provide an example.

3. Why is it necessary to study the order of operations and the laws of operations before you begin solving equations? Please share a specific example.

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Solution Summary

The distributive property is assessed. The sum of the squares are determined.

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1. Could you share a few specific mathematical examples to demonstrate For instance, if I said an important concept of distributive property for the following example is?

Example

4(x+2) = 4x + 8
The usefulness of this property can be illustrated by the following example:
7*(1012) = 7*(1000+12) = (7*1000) + (7*12) = 7000 + 84 = 7084.
So if you split 1012 into 100o and 12, and then use the distributive property, you do not need to work with a large number such as 1012.
The distributive property is often used in connection with coming up with an easier calculation and then make adjustments. For example to compute 4 x 68, 68 can be rounded to 70 = (4 x 70), but 2 groups of 4 must be subtracted from the total 280 to get back to the actual value.
Mathematically this is equal to 4x(68)=4(70-2)=280-8=272
The distributive ...

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