Question

Запишите в виде многочлена стандартного вида выражения: а)(2а-3в)^2 б)(5х-3у)(5х+3у) в)2а^3(а+2в)^2

Answer 1

А) 4а^2-12ав+9в^2
б) 25х^2+15ху-15ху-9у^2=25х^2-9у^2
в) 2а^3(а^2+4ав+4в^2)=4а^5+8ва^4+8в^2а^3

Answer 2

а) (2a - 3b)^2

To expand and simplify the expression (2a - 3b)^2, we can use the formula for squaring a binomial:

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

In this case, we have (2a - 3b)^2. Let's apply the formula:

(2a - 3b)^2 = (2a)^2 - 2(2a)(3b) + (3b)^2

Simplifying further:

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

Therefore, the expression (2a - 3b)^2 can be written in standard form as 4a^2 - 12ab + 9b^2.

б) (5x - 3y)(5x + 3y)

To multiply the binomials (5x - 3y) and (5x + 3y), we can use the formula for multiplying two binomials:

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

In this case, we have (5x - 3y)(5x + 3y). Let's apply the formula:

(5x - 3y)(5x + 3y) = (5x)^2 - (3y)^2

Simplifying further:

(5x - 3y)(5x + 3y) = 25x^2 - 9y^2

Therefore, the expression (5x - 3y)(5x + 3y) can be written in standard form as 25x^2 - 9y^2.

в) 2a^3(a + 2v)^2

To expand and simplify the expression 2a^3(a + 2v)^2, we can use the formula for squaring a binomial:

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

In this case, we have 2a^3(a + 2v)^2. Let's apply the formula:

2a^3(a + 2v)^2 = 2a^3(a^2 + 2 * a * (2v) + (2v)^2)

Simplifying further:

2a^3(a + 2v)^2 = 2a^3(a^2 + 4av + 4v^2)

Therefore, the expression 2a^3(a + 2v)^2 can be written in standard form as 2a^3(a^2 + 4av + 4v^2).