Question

multiply the first expression by the second: 1+x+x²+x³,x³-x²+x-1​

Answer 1

Step-by-step explanation:

x= -1 x³-x²-x+1 => (-1)³-(-1)²-(-1)+1 = > -1-(+1)+1+1 => -1-1+1+1 => -2+2[Minus two(-2) and plus two (+2) gets cancelled] Hence

Answer 2

Step-by-step explanation:

we have to multiply each term in first expression with each term in second expression

$(1 + x + {x}^{2} {x}^{3} ) \times ( {x}^{3} - {x}^{2} + x - 1)$

$1( {x}^{3} - {x}^{2} + x - 1) + x( {x}^{3} - {x}^{2} + x - 1) + {x}^{2} ( {x}^{3} - {x}^{2} + x - 1) + {x}^{3} ( {x}^{3} - {x}^{2} + x - 1)$

${x}^{3} - {x}^{2} + x - 1 + {x}^{4} - {x}^{3} + {x}^{2} - x + {x}^{5} - {x}^{4} + {x}^{3} - {x}^{2} + {x}^{6} - {x}^{5} + {x}^{4} - {x}^{3}$

${x}^{6} + {x}^{4} - {x}^{2} - 1$

x^6+x^4-x^2-1 is the answer