Some important Algebraic formulas for students.

Some important Algebraic formulas for students.

(x+y) ²=x ²+2(x.y)+y ²

^{In this formula we have all terms positive.The x and y terms which are first and last terms of the formula are square terms.The middle term is the two times of the  product of x and y.}

(x - y) ²=x ²-2(x.y)+y ²

In this formula we have x and y terms are positive and square but the middle term is negative but its also two times of the product of x and y.

(x ^2_ y ²) =(x+y)(x-y)

In this formula on left side of formula x and y are square but square is not as a hole.So on right side we can write x and y in the product of (x+y) and (x-y).

(x ²+y ²) =(x+y)(x+y)

In this formula we have both x and y are positive and square on lift side.So it is written as the product of (x+y) and (x+y).

(x-y)³ =(x ³-3 x ² y+3 x y ²- y ³)

In this formula on the right side the first and third terms are positive,the second and fourth terms are negative.The power of  X is reducing and the power of Y  increases. 

(x+y)³ =(x ³+3 x ² y+3 x y ²+y ³)

In this formula on the right sight all the terms are positive.The power of X decreases and the power of y Increases from fist to last term.

X ³+y ³=(x+y)(x ²- x.y+y ²)

In this formula x and y are cube on left side.We write this formula as a product of (x+y) and  

(x ²- x.y+y ²)

X ³- y ³=(x-y)(x ²+x.y+y ²)