Answer:(i) 2x³-4x²-2x(ii) x⁸ -x³ + 2x⁷ -2x² +2x⁵-2
(iii) 2y³+y²-2y⁴-2y³+6y²+3y
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*note: when multiplying two same variables,always add the powers.......
for eg: x³ × x⁴ = x⁷*
Step-by-step explanation:(i) 2x; x²-2x-1
Step : multiply 2x with each term in the other polynomial....
2x × x²-2x -1 = (2x × x²) + (2x × -2x) + (2x × -1)
= 2x3 - 4x² - 2x
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(ii) x⁵-1; x³+2x²+2
Step 1 : multiply x⁵ with each term in the other polynomial....
x⁵ × x³+2x²+2 = (x⁵ × x³) + (x⁵ × 2x²) + (x⁵ × 2)
=. x⁸ + 2x⁷ + 2x⁵ ----> (a)
Step 2: multiply -1 with each term in the other polynomial.......
-1 × x³+2x²+2 = (-1 × x³) + (-1 × 2x²) + (-1 × 2)
= -x³-2x²-2 ------->(b)
Step 3: now add the two products....
(x⁸ + 2x⁷ + 2x⁵) + (-x³-2x²-2)
=x⁸+2x⁷+2x⁵-x³-2x²-2
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Let's follow the same steps to solve part (iii)... (iii) 2y +1 ; y² - 2y³ + 3y
2y × y² - 2y³ + 3y = (2y × y²) + (2y × 2y³) + (2y × 3y)
= 2y³ + 4y⁴ + 6y²
1 × y² - 2y³ + 3y = (1 × y²) + (1 × 2y³) + ( × 3y)
= y² - 2y³ + 3y
(2y³ + 4y⁴ + 6y²) + (y² - 2y³ + 3y)
= 2y³ - 2y³ + 4y⁴ + 6y² -y² +3y
= 4y⁴ + 6y² -y² +3y
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