one of the factors of a square plus b square plus 2ab c square
garrychauhan13:
We have to find common! Am i right ?
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The square of a binomial comes up so often that the student should be able to write the final product immediately. It will turn out to be a very specific trinomial. To see that, let us square (a + b):
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2.
For, the outers plus the inners will be
ab + ba = 2ab.
The order of factors does not matter.
(a + b)2 = a2 + 2ab + b2
The square of any binomial produces the following three terms:
1. The square of the first term of the binomial: a2
2. Twice the product of the two terms: 2ab
3. The square of the second term: b2
The square of every binomial has that form: a2 + 2ab + b2.
To recognize that is to know an essential product in the "multiplication table" of algebra.
(See Lesson 8 of Arithmetic: How to square a number mentally, particularly the square of 24, which is the "binomial" 20 + 4.)
Example 1. Square the binomial (x + 6).
Solution. (x + 6)2 = x2 + 12x + 36
x2 is the square of x.
12x is twice the product of x with 6. (x· 6 = 6x. Twice that is 12x.)
36 is the square of 6.
x2 + 12x + 36 is called a perfect square trinomial -- which is the square of a binomial.
Example 2. Square the binomial (3x − 4).
Solution. (3x − 4)2 = 9x2 − 24x + 16
9x2 is the square of 3x.
−24x is twice the product of 3x· −4. (3x· −4 = −12x. Twice that is −24x.)
16 is the square of −4.
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2.
For, the outers plus the inners will be
ab + ba = 2ab.
The order of factors does not matter.
(a + b)2 = a2 + 2ab + b2
The square of any binomial produces the following three terms:
1. The square of the first term of the binomial: a2
2. Twice the product of the two terms: 2ab
3. The square of the second term: b2
The square of every binomial has that form: a2 + 2ab + b2.
To recognize that is to know an essential product in the "multiplication table" of algebra.
(See Lesson 8 of Arithmetic: How to square a number mentally, particularly the square of 24, which is the "binomial" 20 + 4.)
Example 1. Square the binomial (x + 6).
Solution. (x + 6)2 = x2 + 12x + 36
x2 is the square of x.
12x is twice the product of x with 6. (x· 6 = 6x. Twice that is 12x.)
36 is the square of 6.
x2 + 12x + 36 is called a perfect square trinomial -- which is the square of a binomial.
Example 2. Square the binomial (3x − 4).
Solution. (3x − 4)2 = 9x2 − 24x + 16
9x2 is the square of 3x.
−24x is twice the product of 3x· −4. (3x· −4 = −12x. Twice that is −24x.)
16 is the square of −4.
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