Multiplication of Two Polynomial
To find the product of two polynomial, multiply each term of one polynomial by all the terms of the other polynomial and add all the resulting product –
( x + y ) X ( a + b ) = a X ( x + y ) + b X ( x + y )
or
= x X ( a + b ) + y X ( a + b )
= ax + ay + bx + by
or
= xa + xb + ya + yb
Example – 1) (4a²b⁴ - 3b²cᶟ) X ( 5a⁴c⁵ + 6b²a⁶ )
= {4a²b⁴ X ( 5a⁴c⁵ + 6b²a⁶ )} – { 3b²cᶟ X ( 5a⁴c⁵ + 6b²a⁶ )}
= {(4X5) X (a² X a⁴) X b⁴ X c⁵ } + {(4X6) X (a²X a⁶) X ( b⁴ X b²)} – [{(3 X 5) X a⁴ X b² X (cᶟ X c⁵)} + {(3X6) X (b² X b²) X a⁶ X cᶟ}]
= {(20 X a²⁺⁴ X b⁴ X c⁵) + (24 X a²⁺⁶ X b⁴⁺²)} – {( 15 X a⁴ X b² X cᶟ⁺⁵) + (18 X a⁶ X b²⁺² X cᶟ)}
= 20 a⁶b⁴c⁵ + 24 a⁸b⁶ - 15a⁴b²c⁸ - 18 a⁶b⁴cᶟ (Ans.)