matrix algebra tutorial determinant

1. a 2 + b 2 = (a + b) 2 - 2ab 2. a 2 + b 2 = (a - b) 2 + 2ab 5. (a + b) 2 = (a - b) 2 + 4ab 7. (a + b + c) 2 = a 2 + b 2 + c 2 + 2 (ab + bc + ca) 8. (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 = a 3 + b 3 + 3ab (a + b) 9. (a - b) 3 = a 3 - 3a 2 b + 3ab 2 - b 3 = a 3 - b 3 ..

If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If the polynomial can be expressed as the difference of two squares, we use a 2 - b 2..

If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial..

If all the terms of the polynomial have a common factor, we take out the common factor and factorise. If the polynomial can be expressed as the difference of two squares, we use a 2 - b 2 = (a + b) (a - b)..

(i) Common factors (ii) By expressing as difference of squares (iii) By grouping (iv) Trinomials (v) Sum or difference of cub..

8a 3 b - 6a 2 b 2 = 2a 2 b (4a - ..

Expressions of the form ax 2 + bx + c are called trinomialsExpressions of the form ax 2 + bx + c are called trinomi..

x 2 + 8x + 15 = x 2 + 5x + 3x + 15 (after noticing that 5 + 3 = 8 and 5 3 = 15) = x(x +5) + 3(x + 5) = (x + 5) (x + 3) Resolve into factors: x 2 - 15x + 56 x 2 - 15x + 56 Take factors of 56 having their sum = -15 They are -8, -7. \ x 2 - 15x + 56 = x 2 - 7x - 8x + 56 \ x 2 - 15x +..

x 2 - 2x - 48 = x 2 - 8x + 6x - 48 = x(x - 8) + 6(x - 8) = (x - 8) (x + 6) When the coefficient of the highest power is not unity. i.e., type ax 2 bx c, when and b and c are integers. Multiply (3x + 2) (x + 4) and consider the result so obtained. = 3x (x + 4) +2 (x + 4) = 3x 2 + 12x..

A formula is formed by using:A formula is formed by using: (a) mathematical symbols and variables (b) given conditions, and (c) simplification. Some well known formulae are listed below: Area of a rectangle A = l x b A = Area l = Length b = Breadth Perimeter of a rectangle P = 2(l + b) P = Perimete..