Examples:
 Expand, (x + 2y + 3z)(x^{2} + 4y^{2} + 9z^{2}  2xy  6yz  3xz).
Given that, (x + 2y + 3z)(x^{2} + 4y^{2} + 9z^{2}  2xy  6yz  3xz),
This is in the form of, (a + b + c)(a^{2} + b^{2} + c^{2}  ab  bc  ca) = a^{3} +
b^{3} + c^{3}  3abc.
Here a = x, b = 2y and c = 3z.
= (x)^{3} + (2y)^{3} + (3z)^{3}  3.x.2y.3z
= x^{3} + 8y^{3} + 27z^{3}  18xyz
 Expand, (7x + 3)(4x+2).
Given that, (7x + 3)(4x+2).
This is in the form of (ax + b)(cx + d) = (ac)x^{2} + (ad + bc)x + bd
Here a = 7, b = 3, c = 4 and d = 2.
= (7 * 4)x^{2} + (7*2 + 4*3)x + 6
= 28x^{2} + 26x + 6
 Expand, (x+3)(x+2)(x+1).
Given that, (x+3)(x+2)(x+1).
Formula for this is , (x+a)(x+b)(x+c) = x^{3} + (a+b+c)x^{2} + (ab + bc + ca)x + abc
Here, a = 3, b = 2 and c = 1
= x^{3} + (a+b+c)x^{2} + (6+2+3)x + 3.2.1
= x^{3} + 6x^{2} + 11x + 6
Directions: Solve the following problems. Also write at least 10 examples of your own.
