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more … Expand is when we multiply to remove the ( ) But we have to do it the right way! Example: To expand 3(a+b) we multiply 3 by (a+b) to get 3a + 3b.
Expand is defined as to increase in size, unfold or spread out. An example of expand is someone making friends at a party. An example of expand is a pregnant woman’s belly. An example of expand is someone gathering more knowledge about a topic. … To make greater in size, bulk, scope, etc.; enlarge; dilate; extend.
Standard Form | Expanded Form | |
---|---|---|
20,37,81,405 | = | 20,00,00,000 + 0 + 30,00,000 + 7,00,000 + 80,000 + 1,000 + 400 + 0 + 5 |
100 +00 +0 is your answer.
To expand double brackets we multiply every term in the first bracket, by every term in the second bracket.
The expanded form of 10,000 is 10000+0+0+0+0. In the number 10,000, there are zero thousand, zero hundred, zero tens and zero ones.
to increase in extent, size, volume, scope, etc.: Heat expands most metals. He hopes to expand his company. to spread or stretch out; unfold: A bird expands its wings. to express in fuller form or greater detail; develop: to expand a short story into a novel.
1 : to open up : unfold. 2 : to increase the extent, number, volume, or scope of : enlarge. 3a : to express at length or in greater detail.
Expansion is the process of becoming greater in size, number, or amount.
Function | Summation Expansion | Comments |
---|---|---|
e | e= 1 / n! = 1/1 + 1/1 + 1/2 + 1/6 + … | see constant e |
e ^{–}^{1} | = (-1) ^{n} / n! = 1/1 – 1/1 + 1/2 – 1/6 + … | |
e ^{x} | = x^{n} / n! = 1/1 + x/1 + x^{2} / 2 + x^{3} / 6 + … |
A series expansion is a representation of a particular function as a sum of powers in one of its variables, or by a sum of powers of another (usually elementary) function . Here are series expansions (some Maclaurin, some Laurent, and some Puiseux) for a number of common functions.
To convert 112 in Roman Numerals, we will write 112 in the expanded form, i.e. 112 = 100 + 10 + 1 + 1 thereafter replacing the transformed numbers with their respective roman numerals, we get 112 = C + X + I + I = CXII.
To convert 109 in Roman Numerals, we will write 109 in the expanded form, i.e. 109 = 100 + (10 – 1) thereafter replacing the transformed numbers with their respective roman numerals, we get 109 = C + (X – I) = CIX.
In this example, 3 x 1,000 = 3,000; 0 x 100 =0; 4 x 10 = 40; and 7 x 1 = 7. Your expanded format is correct because 3,000+0+40+7=3,047, which is the standard form of the number.
i d a d m m m Sample answer: Since zero has no value, it does not need to be included when writing a number in expanded form.
To simplify a term written in an expanded form, multiply the numbers together and omit all multiplication signs. Note that it is conventional to place the resultant number (called a coefficient) in front of the pronumerals (letters).
(a +b)2 = a2 + 2ab + b2.
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