Perform the following operations:

a) $(2x^{2}y-3x)(-6y+2xy)-(xy+4y)(-3x+1)$

b) $-7a(ab+2a^2{b}^3)+(3a-5b)(4b-8a)$

c) $5x^{2}y(-2x+4y)-(2x^{3}y-7x^2{y}^2)+4x^2{y}^2-xy$

d) $(4\sqrt{3}x-\sqrt{3}y)(3\sqrt{2}x-\sqrt{3}y)-(3\sqrt{2}x-\sqrt{3}y)(4\sqrt{2}x+\sqrt{3}y)$

Calculate the numerical value of the following expressions:

a) $(\frac{1}{a}+6a)·\frac{2}{3}$ for $a=-3$

b) $(-2x^{2}y{z}^4{)}^2$ for $x=\frac{1}{2},y=-2,z=2$

c) $2b^2-2d+3e^3$ for $b=-3,d=\frac{-1}{5},e=\frac{1}{2}$

Write the expression describing the area of the ADCFE pentagon in the simplest form.

R1ARHQFEEiJUn1

Rysunek prostokąta A B C D o bokach długości 3x dodać 1 i 3x odjąć 1. Z prostokąta odcięto trójkąt prostokątny B E F o przyprostokątnych równych x odjąć 3 oraz x dodać 2 i otrzymano pięciokąt A D C F E.

Number M is a three‑digit number, whose hundreds digit is x, the tens digit is y and the units digit is z. Number K was obtained by exchanging the tens digit with the units digit in number M.

Write the expression $M·K$ in the simplest form.

An extra task:

Prove that the equation below is true for any x.

$x(x-4)+4x-4=(x-2)(x+2)$

Grandma Krysia gave her granddaughter Julia a recipe for a tasdeliciousty apple pie. She told her to take x grams of grated apples, add $\frac{1}{7}x$ grams of butter, $\frac{1}{3}x$ grams of flour, $\frac{1}{5}x$ grams of sugar and $\frac{1}{12}$ kilograms of eggs. Julia prepared 1,8 kg of grater apples. How many kilograms of other ingredients does she have to prepare?

The rectangle has the sides that are equal to $2x+\; 4$ and $x–\; 2.$

The right‑angled triangle has the cathetuses equal to $2x+\; 2$ and $x-\; 5.$

Which polygon has the greater area? By how much?

Describe the solution in English.