word problem of multipling polynomial

Question

multiplying polynomials

Answer 1

To multiply two polynomials, take the individual terms of one polynomial and multiply each term by the whole of the other polynomial using the distributive quality.

(a_nxⁿ+a_n-1x^n-1+...+a₂x²+a₁x+a₀)(b_mx^m+b_m-1x^m-1+...+b₂x²+b₁x+b₀)=

a_nxⁿ(b_mx^m+b_m-1x^m-1+...+b₂x²+b₁x+b₀)+a_n-1x^n-1(b_nxⁿ+b_n-1x^n-1+...+b₂x²+b₁x+b₀)+...=

a_nb_mx^m+n+a_nb_m-1x^m+n-1+...+a_nb₂xⁿ⁺²+a_nb₁xⁿ⁺¹+a_nb₀xⁿ+...

EXAMPLE

(2x²-3x+1)(x³-4x²+5x-6)=

2x²(x³-4x²+5x-6)-3x(x³-4x²+5x-6)+(x³-4x²+5x-6)=

2x⁵  -8x⁴  +10x³-12x²

       -3x⁴  +12x³-15x²+18x

                    x³   -4x²  +5x-6=

2x⁵-11x⁴+23x³-31x² +23x-6.

Note that vertically aligning like powers of x helps when adding the terms. Make sure you have the correct signs in front of each term.