Class 10 Mathematics formulas Algebra Formulas

Class 10 Mathematics formulas

Algebra Formulas

(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b) (a – b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – xz)

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The word mathematics

The word mathematics comes from the ancient Greeks and is derived from the word máthēma, meaning "that which is learnt," according to Douglas R. Harper, author of the "Online Etymology Dictionary(opens in new tab)." The ancient Greeks built on other ancient civilizations’ mathematical studies, and they developed the model of abstract mathematics through geometry. Greek mathematicians were divided into several schools, as outlined by G. Donald Allen, professor of Mathematics at Texas A&M University in his paper, "The Origins of Greek Mathematics(opens in new tab)": In addition to the Greek mathematicians listed above, a number of other ancient Greeks made an indelible mark on the history of mathematics, including Archimedes, most famous for the Archimedes' principle around the buoyant force; Apollonius, who did important work with parabolas; Diophantus, the first Greek mathematician to recognize fractions as numbers; Pappus, known for his hexagon t...

In the 17th century, Isaac Newton in England and Gottfried Leibniz in Germany independently developed the foundations for calculus, Carl B.

In the 17th century, Isaac Newton in England and Gottfried Leibniz in Germany independently developed the foundations for calculus, Carl B. Boyer, a science historian, explained in " The History of the Calculus and Its Conceptual Development (opens in new tab) " (Dover Publications, 1959). Calculus development went through three periods: anticipation, development and rigorization. In the anticipation stage, mathematicians attempted to use techniques that involved infinite processes to find areas under curves or maximize certain qualities. In the development stage, Newton and Leibniz brought these techniques together through the derivative (the curve of mathematical function) and integral (the area under the curve). Though their methods were not always logically sound, mathematicians in the 18th century took on the rigorization stage and were able to justify their methods and create the final stage of calculus. Today, we define the derivative and integral in te...

What is the Mathematics??

What is Mathematics? Mathematics is the science and study of quality, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Through abstraction and logical reasoning mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematic...

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