Your task is to notice how to multiplying an algebraic sum by a monomialmultiplying an algebraic sum by a monomialmultiplying an algebraic sum by a monomial using the distributive property of multiplication over additiondistributive property of multiplication over additiondistributive property of multiplication over addition.

R13dttxgeDqia1

Geogebra aplet - mnożenie sumy algebraicznej przez jednomian. Galeria z opisami alternatywnymi poniżej.

Geogebra aplet - mnożenie sumy algebraicznej przez jednomian. Galeria z opisami alternatywnymi poniżej.

Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/D1C0gLTaX

RMXgZBXVEGb251

Na ekranie są dwa prostokąty styczne bokiem a. Pierwszy o wymiarach a x b,drugi o wymiarach a x c. Wymiary a = 12, b = 5, c = 5. Obok zapisy ab + ac = a(b + c) = ?, 2x^2(x - 4) = 2x^3 - ?x, -y^2 + 5y^3 = y^2(?y - ?).

Rr1xHcM92J62r1

Na ekranie są dwa prostokąty styczne bokiem a. Pierwszy o wymiarach a x b,drugi o wymiarach a x c. Wymiary a = 11, b = 12, c = 7. Obok zapisy ab + ac = a(b + c) = ?, 2x^2(x - 4) = 2x^3 - ?x, -y^2 + 5y^3 = y^2(?y - ?).

Convert the products $-3x^2(3+7x),8ab(3a^2-2b^3)$ into sums.

Use the following formulaformulaformula.

Multiply the monomial by the following algebraic sums.

a) $2x^{2}y(-4,5x^3{y}^2 + 2{\mathrm{xy}}^2 + y)$

b) $-\frac{1}{4}ab(\frac{1}{2}a{b}^3-\frac{4}{17}a+3a^4{b}^2)$

c) $-\mathrm{2,5}{k}^2{l}^3(\mathrm{1,2}{\mathrm{kl}}^2 + 2l^3 – 3,5k^4 - \mathrm{kl})$

Fill in the blanks in such a way that the following equations are correct.

Match the following operations and the corresponding results.

a) $2ab(-3a{b}^2+a^{2}b)$

b) $-a^2(6ab-\sqrt{9}a{b}^2)$

c) $0,5b(\sqrt{36}a{b}^3+4ab)$

d) $-\sqrt{\frac{1}{9}}a\left(6a^2 + 9b^2\right)$

1. $-6a^{3}b+2a^3{b}^2$

2. $3a{b}^4+2a{b}^2$

3. $-6a^2{b}^3+2a^3{b}^2$

4. $-2a^3-3a{b}^2$

There are 18 animals in the backyard: x are hens and the other are dogs. How many legs do all the animals have?

The shorter base of the trapezoid has the length x + 3. The longer one is longer by 5y. The altitude equals 3xy. Calculate the area of the trapezoid.

The longer side of the parallelogram has the length of 4 and the altitude of this side has the length of 8 - x. Write the algebraic expression illustrating the area of the parallelogram.

Calculate the area of the rectangle whose one side has the length of 4x and the other is shorter by z.

Give your solution in English.