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### Grade 8 - Mathematics7.33 Special Products: (a+b+c) (a2+b2+c2-ab-bc-ca)

#### Formula : (a+b+c) (a2+b2+c2-ab-bc-ca)= a3+b3+c3-3abc

Example:
Find the product of (2x+2y+z) (4x2+4y2+z2-4xy-2yz-2xz).
Solution:
Using above formula,
(a+b+c) (a2+b2+c2-ab-bc-ca) = (2x+2y+z) (4x2+4y2+z2-4xy-2yz-2xz).
= (2x)3+(2y)3+(z)3-3.2x.2y.z
= 8x3+8y3+z3-12xyz

Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: Find the product of (4x+y+z) (16x2+y2+z2-4xy-yz-4xz). 64x3+y3+z3-12xyz64x3+y3+z3-9xyz64x3+y3+z3-18xyz Q 2: Find the product of (4x+2y+z) (16x2+4y2+z2-8xy-2yz-4xz).64x3+8y3+z3-24xyz64x3+8y3+z3-18xyz64x3+8y3+z3-21xyz Q 3: Find the product of (3x+2y+z) (9x2+4y2+z2-6xy-2yz-3xz). 27x3+8y3+z3-12xyz27x3+8y3+z3-9xyz27x3+8y3+z3-18xyz Q 4: Find the product of (3x+y+z)(9x2+y2+z2-3xy-yz-xz). 27x3+y3+z3-3xyz27x3+y3+z3+9xyz27x3+y3+z3-9xyz Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!

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