Advertisements
Advertisements
Question
Find the following product:
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
Advertisements
Solution 1
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= 2x(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) – y(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) + 3z(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= 8x3 + 2xy2 + 18xz2 + 4x2y + 6xyz – 12x2z – 4x2y – y3 – 9yz2 – 2xy2 – 3y2z + 6xyz + 12x2z + 3y2z + 27z3 + 6xyz + 9yz2 – 18xz2
= 8x3 + (2xy2 – 2xy2) + (18xz2 – 18xz2) + (4x2y – 4x2y) + (6xyz + 6xyz + 6xyz) + (–12x2z + 12x2z) – y3 + (–9yz2 + 9yz2) + (–3y2z + 3y2z) + 27z3
= 8x3 + 18xyz – y3 + 27z3
= 8x3 – y3 + 27z3 + 18xyz
Solution 2
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= (2x – y + 3z)[(2x)2 + (–y)2 + (3z)2 – (2x)(–y) – (–y)(3z) – (2x)(3z)]
= (2x)3 + (–y)3 + (3z)3 – 3(2x)(–y)(3z) ...[Using identity, (a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc]
= 8x3 – y3 + 27z3 + 18xyz
APPEARS IN
RELATED QUESTIONS
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + x + 1
Determine the following polynomial has (x + 1) a factor:
x4 + x3 + x2 + x + 1
Find the Factors of the Polynomial Given Below.
2x2 + x – 1
Factorize the following polynomial.
(x2 – 6x)2 – 8 (x2 – 6x + 8) – 64
One of the factors of (25x2 – 1) + (1 + 5x)2 is ______.
Show that x + 3 is a factor of 69 + 11x – x2 + x3.
Determine which of the following polynomials has x – 2 a factor:
3x2 + 6x – 24
Factorise:
84 – 2r – 2r2
Without finding the cubes, factorise:
(x – 2y)3 + (2y – 3z)3 + (3z – x)3
If both x – 2 and `x - 1/2` are factors of px2 + 5x + r, show that p = r.
