Analyze an interactive drawing. Pay attention to the way how the multiplication of the algebraic sumalgebraic sumalgebraic sum by the number and the multiplication of algebraic sum by the algebraic sum are performed. Formulate the appropriate conclusions.

Write in the form of an algebraic expression:

a) the sum of the doubled variable x and the tripled variable y,

b) the difference in the number of a and the doubled sum of x and y variables,

c) the product of the square of the number a and the number b,

d) the quotient of the sum of the numbers a and b by their difference.

Bring the expression to the simplest formsimplest formsimplest form:

a) $7m^2-(-1)\cdot [4m^2-3m-[m^2-4m]]$

b) $\left(2m^2+6nm+5\right)·3nm-5nm$

c) $\left(-5a^3+15a^2-25a\right):(-5a)+2$

d) $\left(-2b^2+6b^3·c^2-8b^4·c^3\right):\left(-2b^2\right)$

Bring the expression to the simplest formsimplest formsimplest form, then calculate its numerical value for the given variable values:

a) $4\cdot (\frac{1}{2}x-2)+(-16x^2+4x):(-4x)-(-5x+3)\cdot (-1)$

$x=\frac{2}{3}$

b) $(12a^4{b}^4-9a^2{b}^3):(-3a^{2}b)-(2+3a^{2}b)\cdot b^2$

$a=-1$, $b=-2$

Do the multiplication:

a) $(x+2)(y-5)$

b) $(b+4)(5-3b)$

c) $-2(2x+3)(6-5x)$

Bring the expression to the simplest formsimplest formsimplest form:

a) $(a-b)(2a+3b)+(a+3b)(-a+4b);$

b) $–(n+5m)(3n+m-4)+(6n-3m)(m-n+2)-3\left(n^2+m^2\right).$

An extra task:

Simplify fractions. Provide the necessary assumptions

a) $\frac{x(x+2)}{2·x};$

b) $\frac{(3·m·n-m^2)}{3·m·n}.$

Calculate the value of the expression $(5x+2)(3x-4)+5x(7-5x)$ for $x=\frac{9}{10}.$

Describe in English how to multiply the algebraic sum by the algebraic sum.