Question

Умножить многочлен на одночлен 1)(2a+3b)(4ab) = 2a * 4ab +3b * 4b = 2)(5a-6b) (-7ab)=5a*(-7ab)-6b = 3)(1/2a^2+1/3b^2)(1/4a^2b^2)= 3)(0,2x^2+0,3xy - 0,4xy^2)(-30xy) =

Answer 1

1) 8 $а^{2}$b+12 $b^{2}$
2) -35 $a^{2}$b-6b
3) $\frac{1}{8} a^{4} b^{2} + \frac{1}{12} a^{2} b^{4}$
4)  $-6 x^{3} y-3 x^{2} y^{2} +12 x^{2} y^{3}$

Answer 2

Let's simplify the multiplication step by step:

1. (2a + 3b)(4ab) = 2a * 4ab + 3b * 4ab = 8a^2b + 12ab^2

2. (5a - 6b)(-7ab) = 5a * (-7ab) - 6b * (-7ab) = -35a^2b + 42ab^2

3. (1/2a^2 + 1/3b^2)(1/4a^2b^2) = (1/2a^2)(1/4a^2b^2) + (1/3b^2)(1/4a^2b^2) = 1/(8a^4b^2) + 1/(12a^2b^4) (To simplify further, we need a common denominator) = (3a^2 + 2b^2)/(24a^4b^2)

Note: In the last step, I'm assuming that the given polynomial expression (1/2a^2 + 1/3b^2)(1/4a^2b^2) is intended to be written as (1/(2a^2) + 1/(3b^2))(1/(4a^2b^2)). If the coefficients 0.2, 0.3, and 0.4 in your question are intended to represent decimal values, please let me know, and I will adjust the calculation accordingly.