Wikipedia
the product of any two binomials is a binomial? : This article does not cite any references or sources. ... The binomial a2 b2 can be factored as the product of two other binomials: ..... More from Wikipedia
Binomial Theorem
1. A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. 2. A statement involving natural number n is generally denoted by P(n). 3. A binomial is an algebraic ex..
Binomial Theorem
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expressi..
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expressi.. Access full lesson containing this video at: www.yourteacher.com Students learn that a trinomial in the form x^2 + bx + c (where c is positive), such as x^2 + 7x + 10, can be factored as the product of two binomials, in this case (x + 5)(x + 2). The first term in each binomial comes from the factors of x^2, x and x. The second term in each binomial comes from the factors of the constant term, +10, that add to the coefficient of the middle term, +7, which in this case are +5 and +2. ...
Access full lesson containing this video at: www.yourteacher.com Students learn that a trinomial in the form x^2 + bx + c (where c is negative), such as x^2 + 6x -- 27, can be factored as the product of two binomials, in this case (x + 9)(x -- 3). The first term in each binomial comes from the factors of x^2, x and x. The second term in each binomial comes from the factors of the constant term, --27, that add to the coefficient of the middle term, +6, which in this case are +9 and --3. ...
Question :
Answer : The product of two binomials will be a binomial if and only if the two are conjugates. (a + b)(c + d) = ac + ad + bc + bd If ac + ad = 0 c = - d and the 2nd term is no longer a binomial. If ac + bc = 0 a = - b and the 1st term is no longer a binomial If ac + bd = 0 ac = - bd (a + b)(c + d) = ad + bc c = - bd/a (a + b)(- bd/a + d) = ad - b^2d/a (a + b)(- bd + ad)/a = (a^2d - b^2d)/a (a + b)(- b + a)d/a = (d/a)(a^2 - b^2) (a + b)(a - b) = (a^2 - b^2) In the same way, one can show that the only other product which is a binomial is (c + d)(c - d) = c^2 - d^2.. More from Yahoo Answers
Answer : The product of two binomials will be a binomial if and only if the two are conjugates. (a + b)(c + d) = ac + ad + bc + bd If ac + ad = 0 c = - d and the 2nd term is no longer a binomial. If ac + bc = 0 a = - b and the 1st term is no longer a binomial If ac + bd = 0 ac = - bd (a + b)(c + d) = ad + bc c = - bd/a (a + b)(- bd/a + d) = ad - b^2d/a (a + b)(- bd + ad)/a = (a^2d - b^2d)/a (a + b)(- b + a)d/a = (d/a)(a^2 - b^2) (a + b)(a - b) = (a^2 - b^2) In the same way, one can show that the only other product which is a binomial is (c + d)(c - d) = c^2 - d^2.. More from Yahoo Answers
Question : This is a homework question just that i need a little more explanation from others
Answer : When it is the difference of squares. For instance (A+B)(A-B)=A^2-B^2 if there are no imaginary parts to it (i). Let's solve it out the real way to see if it actually yields that. (X-4)(X+4)=??? (X-4)(X+4)=X^2-4X+4X-16 (X-4)(X+4)=X^2-16 In General Form this is (A+B)(A-B)=??? (A+B)(A-B)=A^2+AB-AB-B^2 (A+B)(A-B)=A^2-B^2 This is called the difference of squares and works no matter what A and B are unless there are imaginary parts... More from Yahoo Answers
Answer : When it is the difference of squares. For instance (A+B)(A-B)=A^2-B^2 if there are no imaginary parts to it (i). Let's solve it out the real way to see if it actually yields that. (X-4)(X+4)=??? (X-4)(X+4)=X^2-4X+4X-16 (X-4)(X+4)=X^2-16 In General Form this is (A+B)(A-B)=??? (A+B)(A-B)=A^2+AB-AB-B^2 (A+B)(A-B)=A^2-B^2 This is called the difference of squares and works no matter what A and B are unless there are imaginary parts... More from Yahoo Answers
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