<span>binomial </span>is an algebraic expression containing 2 terms. For example, (x + y) is a binomial.
We sometimes need to expand binomials as follows:
(a + b)0 = 1
(a + b)1 = a + b
(a + b)2 = a2 + 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3
<span>(a + b)4</span> <span>= a4 + 4a3b</span><span> + 6a2b2 + 4ab3 + b4</span>
<span>(a + b)5</span> <span>= a5 + 5a4b</span> <span>+ 10a3b2</span><span> + 10a2b3 + 5ab4 + b5</span>
Clearly, doing this by direct multiplication gets quite tedious and can be rather difficult for larger powers or more complicated expressions.
Pascal's Triangle
We note that the coefficients (the numbers in front of each term) follow a pattern. [This was noticed long before Pascal, by the Chinese.]
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
You can use this pattern to form the coefficients, rather than multiply everything out as we did above.
The Binomial Theorem
We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.
<span>Properties of the Binomial Expansion <span>(a + b)n</span></span><span><span>There are <span>\displaystyle{n}+{1}<span>n+1</span></span> terms.</span><span>The first term is <span>an</span> and the final term is <span>bn</span>.</span></span><span>Progressing from the first term to the last, the exponent of a decreases by <span>\displaystyle{1}1</span> from term to term while the exponent of b increases by <span>\displaystyle{1}1</span>. In addition, the sum of the exponents of a and b in each term is n.</span><span>If the coefficient of each term is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we obtain the coefficient of the next term.</span>
Answer:
Side A is 4
Step-by-step explanation:
3x-11=x+23
-x -x
2x-11=23
+11 +11
2x=34
x=17
3(17)-11 17+23
=40 =40
explanation ;
you would equal them because they are congruent . & you substitute x for 17 in each equation to find out the degrees of both of the angles :)
HL Theorem would prove these two triangles are congruent.
<span>Which
of the following is 7.4 kilograms?
=> 740 000 mg
=> 740 g
=> 74 hg
=> 74 000 cg
Let’s base on the Unit of measurement or conversion.
=> 740 000 mg
In every 1 kilogram is equals to 1 000 000
=> 7.4 kg * 1 000 000 mg = 7 400 000 mg
It’s not the correct Answer
=> 740 g
In every 1 kg is equals to 1 000 grams
=> 7.4 * 1000 = 7 400 grams
Thus, it’s not the correct answer
=> 74 hg
In every 1kg is equals to 10 hectograms
=> 7.4 kg x 10 = 74hg
Thus, this is the correct answer
=> 74 000 cg
In every 1kg is equals to 100 000
=> 7.4 * 100 000 = 740 000
not the correct answer.
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