write all the terms of the algebraic expression with examples
Answers
Answer:
Example of Trinomials Identity : (a + b + c)2 = a2 + b2 + c2 + 2 · a · b + 2 · a · c + 2 · b · c
(x2 − x + 1)2 = (x2)2 + (−x)2 + 12 + 2 · x2 · (−x) + 2 x2 · 1 + 2 · (−x) · 1
= x4 + x2 + 1 − 2x3 + 2x2 − 2x
= x4− 2x3 + 3x2 − 2x + 1
Step-by-step explanation:
Apart from the algebraic identities mentioned above one more useful identity frequently used is the one given by the equation:
(x – y) (x – z) = x2 – (y + z) x + yz
Notice that, in the above given equation, on the right side, the sum total, say S = y+z and the product, say P = yz of y and z are present. When the equation is expressed in a form x2 – Sx + P, and S and P are representing a sum and product of two numericals or expressions, this expression is known as second degree trinomial which is to say x2 – Sx + P Therefore, when we write the above given example in reverse it can be seen as factorization for second degree trinomials, that is to say: x2 – Sx + P= (x – y) (x – z),
Here, S= y + z and P = yz. The above noted factorization method is also called Viète’s formula, as a commemoration to François Viete, the French mathematician. He was a sixteenth century mathematician who pioneered in using alphabets to represent variables. He is often called the father of algebra.