Question

(3а^2b-4ab^3):(5ab); 2) (2c^5b^4+3c^4b^3):(-3c^4b^3); 3) (-27k^4l^5+21k^3l^2):(-10k^3l^2);4) (-a^5b^3+3a^6b^2):(4a^4b^2)

Answer 1

1) (3a²b - 4ab³) : (5ab) =ab(3a - 4b²) : 5ab = (3a - 4b²) : 5;  2) (2c⁵b⁴ + 3c⁴b³) : ( -3c⁴b³) = c⁴b³( 2cb + 3) : ( -3c⁴b³) = - 1/3 (2bc + 3) = - 2/3bc - 1;  3) ( - 27(k⁴¹)⁵ + 21(k³¹)²) : ( -10(k³¹)² = ( - 27k²⁰⁵ + 21k⁶²) :- 10k⁶² = 2,7k¹⁴³ - 2,1;   4) ( - a⁵b³ + 3a⁶b²) : 4a⁴b² = - ( a⁵b²(b + 3a)) : 4a⁴b² = - 0,25a(b + 3a)

Answer 2

To simplify each expression, we'll perform the divisions step by step:

1. (3a^2b - 4ab^3) : (5ab)

Step 1: Factor out the common term 'ab' from the numerator. (3a^2b - 4ab^3) = ab(3a - 4b^2)

Step 2: Divide the factored expression by the denominator '5ab': (ab(3a - 4b^2)) : (5ab) = (3a - 4b^2) : 5

Final result: (3a - 4b^2) / 5

2. (2c^5b^4 + 3c^4b^3) : (-3c^4b^3)

Step 1: Factor out the common term 'c^4b^3' from the numerator. (2c^5b^4 + 3c^4b^3) = c^4b^3(2c + 3)

Step 2: Divide the factored expression by the denominator '-3c^4b^3': (c^4b^3(2c + 3)) : (-3c^4b^3) = -(2c + 3) : 3

Final result: -(2c + 3) / 3

3. (-27k^4l^5 + 21k^3l^2) : (-10k^3l^2)

Step 1: Factor out the common term '-k^3l^2' from the numerator. (-27k^4l^5 + 21k^3l^2) = -k^3l^2(27k^2l^3 - 21)

Step 2: Divide the factored expression by the denominator '-10k^3l^2': (-k^3l^2(27k^2l^3 - 21)) : (-10k^3l^2) = (27k^2l^3 - 21) : 10

Final result: (27k^2l^3 - 21) / 10

4. (-a^5b^3 + 3a^6b^2) : (4a^4b^2)

Step 1: Factor out the common term 'a^4b^2' from the numerator. (-a^5b^3 + 3a^6b^2) = a^4b^2(-a - 3a^2)

Step 2: Divide the factored expression by the denominator '4a^4b^2': (a^4b^2(-a - 3a^2)) : (4a^4b^2) = (-a - 3a^2) : 4

Final result: (-a - 3a^2) / 4