Question

3. A polynomial of degree 3 is called a cubic polynomial.
Examples (i) 4x3 + 3x2 + 2x +1, -6x 3 + 4x2 +5, 7a3 - 8a+9 and 8a- 3
are cubic polynomials in one variable.
(ii) 2x3 + 3y2 + xy and 12x²y +9y3 – 5xy2 + 7 are cubic
polynomials in two variables.
(iii) 3x²y-5yz? and 8 xyz +6yz2+9xz2 - xy +5 cubic
polynomials in three variables.​

Answer 1

Answer:

(i) (x+y+z)(x-y-z).

(x+y+z)(x−y−z) ( x + y + z ) ( x - y - z ).

Expand

(x+y+z)(x−y−z) ( x + y + z ) ( x - y - z ) by multiplying each term in term in the first expression by each term in the second expression.

Simplify terms

x²-y²-yz-zy-z²

Subtract zy from -yz

x²-y²-2yz-z²

(ii) x²(x-3y²)-xy(y²-2xy)-x(y³-5x²)

x³-3x²y²-xy³+2x²y²-xy³+5x³

 

(iii) -7x²-2x(-7x²-2x)