Using Pascal's triangle, expand `(1+x)^4` in powers of x.

Expand: (4x+3y)^3

Expand: (4x+5y)^3

Expand: (4/5x-2)^3

Expand: (2x-2/x)^3

If the coefficient of x^(3) and x^(4) in the expansion of (1+ax+bx^(2)) (1-2x)^(18) in power of x are both zero, then (a,b) is equal to

The coefficient of the middle term in the binomial expansion in powers of x of (1+ alpha x)^4 and of (1-alpha x)^6 is the same, if alpha equals :

When the determinant |{:(cos2x,,sin^(2)x,,cos4x),(sin^(2)x,,cos2x,,cos^(2)x),(cos4x,,cos^(2)x,,cos 2x):}| expanded in powers of sin x, then the constant term in that expression is

Expand (1-x/2)^(-1//2) when | x | < 2.

The sides of a triangle are 3x + 4y, 4x + 3y and 5x+5y units, where x gt 0, y gt 0 . The triangle is

Let us observe Pascal triangle 1:1=11^0 2:11=11^1 3:121=11^2 . Form a conjecture for row 4 and row.