a) Determine the coefficient of x^3*y^4 in the expansion of (2x+y)^12. b) Determine the coefficient of x^2*y^3*z^2 in the expansion of (2x-y+3z)^7.

Q: Find the derivative of function f given by S(1) = =! X-1 3 x+3'

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Q: 3. What is the leading coefficient in this polynomial ? -7x^3 + 5x^2 + 8x^4 - 9x^7 - 15 -7 -9 -15

A: From the given equation , first we find the degree of the equation Degree is 7 So the coefficient…

Q: 8. Calculate (x* - 12x³ + 6x² – 9x + 15) + (x + 2) using long division.

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Q: Rationalize the denomi 20 5/10 - 7/5

A: 20510-75

Q: Which of the followings is/are in the expansion of (a+b)^6?

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Q: Evaluate (6 – 5)^2 by working within the parentheses first. Evaluate 6^2 – 5^2. Compare the answer…

A: Evaluate (6 – 5)^2 Evaluate 6^2 – 5^2.

Q: O write the expansion of : (3a+ 2b)$ , (4z – w) , - -→*

A: We have to expand the following expression by using binomial expansion

Q: 4.[4Y²-Y) (Y-2) 5.CxX+1)(x-2)

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Q: Expand in binomial theorem (2x-y)7

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Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

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Q: Find the term that contains x^8 in the expansion of (3x-1)^11

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Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: Which of the following is the factored form of x^3 + 3x^2 – 10x – 24? * - O (x - 4)(x – 3)(x – 2) O…

A: Let f(x) = x3 + 3x2 - 10x - 24

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

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Q: Expand (4-x)^4 by using binomial expansion

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Q: What is the coefficient of x^8 in the expansion of (2+x)^11?

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Q: 7) Use binomial theorem to expand (2x-1)^6

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Q: divide x – 6x² – 9 by x + 6 | 1089 O x³ + 6x² + 42x + 180 + x+6 -x3 – - 6x² + 30x – 180 10 X- 1071 O…

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Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: What is the coefficient of (x^8)(y^12) in the expansion of (y+x)^20

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Q: SHOW THAT 3^2N - 1 IS DIVISIBLE BY 8 FOR ALL POSITIVE INTEGERS.

A: We prove this by induction.