expansions

Working rules for expanding (a + b) n n N: Step 1: The value of index, n implies that there will be n+1 terms in the expansion of (a + b) n . Step 2: Write the first term: n C 0 a n b 0 . Step 3: For the second term, take coefficient as n C 1 , decrea..

Material α / °C Iron 12x10 -6 Copper 17x10 -6 Steel 11x10 -6 Gold 14x10 -6 Pyrex glass 3x10 -6 soft glass 9x10 -6 ' a ' of iron is 12x10 - 6 / 0 C means, if a rod of length 1m is heated through 1 0 C, then length increases by an amount of 12x1..

Use binomial theorem to find the expansion of (1 - x) 5 => 1 - 5x + 10x 2 - 10x 3 - 5x 4 + x 5 or 1- x + x 2 - x 3 + x 4 - x 5 or 1 - 5x + 10x 2 - 10x 3 + 5x 4 - x 5 or 1- x 5..

Approximate (0.99) 30 to the nearest tenth using the first two terms of a binomial expansion. => 0.03 or 0.3 or 0.07 or 0.7..

The dimensions (in inches) of a rectangular metal sheet are in the ratio 3 : 2. Due to the heat the sheet expanded as shown. Perimeter of the sheet after the expansion is 110 inches. What is the percent increase in the perimeter of the sheet? => 22.22 or 24.22 or 22.32 or 23.22..

Find the eighth term in the binomial expansion of ( x - 2) 7 . => -512 or 64 or 256 or -128..

Use binomial theorem to find the expansion of ( x 2 + 2) 4 . => x 8 + 8x 6 + 24x 4 + 32x 2 + 16 or x 8 + 8x 5 + 24x 4 + 24x 2 + 8 or x 8 + 8x 5 + 24x 4 + 24x 2 + 8 or x 8 + 16..

Find the third term in the binomial expansion of (2 + xy ) 4 . => 24 x 3 y 3 or 4 x 2 y 2 or 24 x 2 y 2 or 48 x 2 y 2..

Write the variable part of the term having a coefficient of 4096. in the expansion (4 g - h ) 6 . => x 5 y or x 6 or y 6 or x 3 y 3..

State the number of terms in the expansion of ( x + y ) 6 and give the first and last terms. => 6, x 7 , y 7 or 6, x 6 , y 6 or 7, x 6 , y 6 or 7, x 6 y , xy 6..