Multiplying polynomials

Question

bryyy

Asked: September 23, 20212021-09-23T10:44:45+00:00 2021-09-23T10:44:45+00:00In: Algebra

Multiply the polynomials: (x^4+3x^2-1)(4x^3+x^2-x+3)(x^6-2)

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acedstud · Accepted Answer · 2021-09-23T19:08:11+00:00

Best Answer

acedstud

Multiply two at a time using the distributive property (foil).

Multiply $(x^4+3x^2-1)(4x^3+x^2-x+3)=x^4(4x^3+x^2-x+3)+3x^2(4x^3+x^2-x+3)-(4x^3+x^2-x+3)$

$=4x^{4+3}+x^{4+2}-x^{4+1}+3x^4+12x^{2+3}+3x^{2+2}-3x^{2+1}+9x^2-4x^3-x^2+x-3$

$=4x^7+x^6-x^5+3x^4+12x^5+3x^4-3x^3+9x^2-4x^3-x^2+x-3$

Collect like terms; terms with the same exponent:

$=4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3$

Now, multiply $(4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3)(x^6-2)$

$=x^6(4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3)-2(4x^7+x^6+11x^5+6x^4-7x^3+8x^2+x-3)$

$=4x^{6+7}+x^{6+6}+11x^{6+5}+6x^{6+4}-7x^{6+3}+8x^{6+2}+x^{6+1}-3x^6-8x^7-2x^6-22x^5-12x^4+14x^3-16x^2-2x+6$

$=4x^{13}+x^{12}+11x^{11}+6x^{10}-7x^{9}+8x^{8}+x^{7}-3x^6-8x^7-2x^6-22x^5-12x^4+14x^3-16x^2-2x+6$

Collect like terms; terms with the same exponent

$4x^{13}+x^{12}+11x^{11}+6x^{10}-7x^{9}+8x^{8}-7x^{7}-5x^6-22x^5-12x^4+14x^3-16x^2-2x+6$

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