Special Pattern BinomialsThe following are special multiplications involving binomials that you will want to try to remember. Be sure to notice the patterns in each situation. You will be seeing these patterns in numerous problems. Don’t panic! If you c…

What is Transformation of Axes? (1) Shifting of origin without rotation of axes :Let P ≡ (x, y) with respect to axes OX and OY. Let O’ ≡ (α, β) with respect to axes OX and OY and let P ≡ (x’, y’) with respect to axes O’X’ and O’Y’, where OX and O’X’ are …

How do you Calculate Simple Interest?Simple Interest Interest: Interest is the amount paid in lieu of using some money which is not owned by us.The amount of money deposited, lent or borrowed is called principal (P).The additional money given at the end…

What is an Exponent?ExponentsThe repeated addition of numbers can be written in short form (product form). Examples: Also, we can write the repeated multiplication of numbers in a short form known as exponential form. For example, when 5 is multiplied…

How do you Transpose a Matrix?Transpose of a matrixThe matrix obtained from a given matrix A by changing its rows into columns or columns into rows is called transpose of matrix A and is denoted by AT or A′. From the definition it is obvious that if orde…

What is Logarithmic Series Expansion ?https://www.youtube.com/watch?v=sC8-Kt_NkEY&t=15sLogarithmic SeriesDefinition An expansion for loge (1 + x) as a series of powers of x which is valid only, when |x|<1.Expansion of logarithmic seriesExpansion …

What is the Multinomial Theorem?Multinomial theoremLet x1, x2, …….., xm be integers. Then number of solutions to the equation x1 + x2 +…….. + xm = n  …..(i) Subject to the condition a1 ≤ x1 ≤ b1, a2 ≤ x2 ≤ b2, ……, am ≤ xm ≤ bm  …..(ii) is equal to the c…

What are the Special Types of Matrices?Singular and Non-singular matrix :Any square matrix A is said to be non-singular if |A| ≠ 0, and a square matrix A is said to be singular if |A| = 0. Here |A| (or det(A) or simply det |A| means corresponding determi…

Solving Trigonometric EquationsImportant points to be taken in case of while solving trigonometrical equationsCheck the validity of the given equation, e.g. 2 sin θ – cos θ = 4 can never be true for any θ as the value (2 sin θ – cos θ) can never exceeds…

Binomial Theorem for any Indexhttps://www.youtube.com/watch?v=xMziTBR34_MBinomial theorem for positive integral indexThe rule by which any power of binomial can be expanded is called the binomial theorem. If n is a positive integer and x, y ∈ C then Bin…