Question

Запишите в виде многочлена стандартного вида: а) (2а-3b)^2 b) (a+2b) (a^2-2ab+4b^2)

Answer 1

$a) \;\;(2a-3b)^2=(2a)^2-2*2a*3b+(3b)^2=4a^2-12ab+9b^2\\b)\;\;(a+2b) (a^2-2ab+4b^2)=a^3+(2b)^3=a^3+8b^3$

Answer 2

a) (2a - 3b)^2

To expand the square of the binomial (2a - 3b)^2, we use the formula (a - b)^2 = a^2 - 2ab + b^2.

(2a - 3b)^2 = (2a)^2 - 2(2a)(3b) + (3b)^2 = 4a^2 - 12ab + 9b^2

So, the expanded form of (2a - 3b)^2 is 4a^2 - 12ab + 9b^2.

b) (a + 2b)(a^2 - 2ab + 4b^2)

To multiply the two binomials (a + 2b) and (a^2 - 2ab + 4b^2), we use the distributive property.

(a + 2b)(a^2 - 2ab + 4b^2) = a(a^2 - 2ab + 4b^2) + 2b(a^2 - 2ab + 4b^2)

Now, distribute each term:

= a * a^2 + a * (-2ab) + a * 4b^2 + 2b * a^2 + 2b * (-2ab) + 2b * 4b^2 = a^3 - 2a^2b + 4ab^2 + 2a^2b - 4ab^2 + 8b^3

Now, simplify the expression:

= a^3 + 8b^3

So, the expanded form of (a + 2b)(a^2 - 2ab + 4b^2) is a^3 + 8b^3.