algebra cube expansions

Expansions - We shall discuss expansions of binomials and trinomi..

In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help us to ..

Summary - (a + b) (a - b) = a 2 - b 2 (x + a) (x + b) = x 2 + (a + b)x + ab. (a + b) 3 = a 3 + b 3 + 3ab (a + b) = a 3 + 3a 2 b + 3ab 2 + b 3..

(a + b) 2 = a 2 + 2ab + b 2 (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 - 2ab + b 2 In the above two formulae the middle term = (a + b) (a - b) = a 2 - b 2 (x + a) (x + b) = x 2 + (a + b)x + ab. (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ac (a + b) 3 =..

a) "x is less than y" b) " x is greater than y" c) "x is multiple of 3" d) "x divides y" e) "Cube of x plus the square of y is 25" f) "Triangle x is congruent to triangle y..

Summary - 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..

TutorVista's online Algebra help isn't just about working out a few problems and logging off. Features like regular homework help , and exam prep enable a student to get all the help he/she needs. There is also an extensive library of e-learning material like Algebra question ..

Each edge of a cube is x cm in length. If the length of each edge is increased by 7 cm, then find the binomial expansion that represents the volume of the new cube. => ( x + 7) 3 or ( x - 7) 3 or ( x + 7) 2 or ( x + 7)..

Choose an algebraic sentence for "The cube of the quantity nine less than a number is equal to 64". Use a as the variable. => 3( a - 9) = 64 or ( a - 9) 3 = 64 or 3 a - 9 = 64 or a 3 - 9 = 64..

The last terms in (ii) and (iii) depends upon the fact whether n is even or odd. The binomial theorem for fractional index states that General term For r 0, T r + 1 in the expansion of (1+x) n , |x|<1,n Q is given by If x be so small that its squares and higher powers may be neglected,..