Question

Применяя формулу сокращенного умножения, запишите алгебраическое выражение в виде многочлена стандартного вида: а) (а-b)^2 б) )а-b)(а+b)= в) (х+y)^3= Запишите алгебраическое выражение в виде многочлена: а) (а+5)^2= б) (а + 6)(а - 6)= в) (х - 2)^3= г) (х+3)(х^2 - 3х + 9)= Запишите алгебраическое выражение в виде квадрата или куба двучлена: а) х^2 - 2х + 1= б) х^2 + 6х + 9= в) х^3 + 6х^2 + 12х + 8= г) х^3 - 9х^2 + 27х - 27= Буду очень благодарна!

Answer 1

А)(а-b)²=a²-2ab+b²
б)(a-b)(a+b)=a²-b²
в)(x+y)³=х³+3х²у+3ху²+у³

а)(а+5)²=а²+10а+25
б)(а+6)(а-6)=а²-36
в)(х-2)³=х³-6х2+12у³-8
г)(х+3)(х²-3х+9)=х³+27

а)х²-2х+1=(х-1)²
б)х²+6х+9=(х+3)²
дальше не знаю(

Answer 2

Applying the Formula of Polynomial Multiplication

To apply the formula of polynomial multiplication, we'll use the formula for the square of a binomial and the cube of a binomial to express the given algebraic expressions as standard polynomial forms.

a) Expressing (a-b)^2 in Standard Polynomial Form

The square of a binomial can be expressed using the formula: (a - b)^2 = a^2 - 2ab + b^2.

Therefore, the algebraic expression (a-b)^2 can be written in the standard polynomial form as: (a - b)^2 = a^2 - 2ab + b^2.

b) Expressing (a+b)(a-b) in Standard Polynomial Form

The product of the sum and difference of two terms can be expressed using the formula: (a + b)(a - b) = a^2 - b^2.

Hence, the algebraic expression (a+b)(a-b) can be written in the standard polynomial form as: (a + b)(a - b) = a^2 - b^2.

c) Expressing (x+y)^3 in Standard Polynomial Form

The cube of a binomial can be expressed using the formula: (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3.

Therefore, the algebraic expression (x+y)^3 can be written in the standard polynomial form as: (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3.

d) Expressing (x+3)(x^2-3x+9) in Standard Polynomial Form

The product of a binomial and a trinomial can be expanded using the distributive property.

Hence, the algebraic expression (x+3)(x^2-3x+9) can be expanded to the standard polynomial form as: (x+3)(x^2-3x+9) = x^3 - 3x^2 + 9x + 3x^2 - 9x + 27.

Simplifying further, we get: (x+3)(x^2-3x+9) = x^3 + 6x^2 + 12x + 27.

Expressing Algebraic Expressions as Squares or Cubes of Binomials

a) Expressing x^2 - 2x + 1 as a Square of a Binomial

The expression x^2 - 2x + 1 can be expressed as the square of a binomial using the formula: (a - b)^2 = a^2 - 2ab + b^2.

Therefore, x^2 - 2x + 1 can be written as: (x - 1)^2.

b) Expressing x^2 + 6x + 9 as a Square of a Binomial

The expression x^2 + 6x + 9 can be expressed as the square of a binomial using the formula: (a + b)^2 = a^2 + 2ab + b^2.

Hence, x^2 + 6x + 9 can be written as: (x + 3)^2.

c) Expressing x^3 + 6x^2 + 12x + 8 as a Cube of a Binomial

The expression x^3 + 6x^2 + 12x + 8 can be expressed as the cube of a binomial using the formula for the cube of a binomial.

Therefore, x^3 + 6x^2 + 12x + 8 can be written as: (x + 2)^3.

d) Expressing x^3 - 9x^2 + 27x - 27 as a Cube of a Binomial

The expression x^3 - 9x^2 + 27x - 27 can be expressed as the cube of a binomial using the formula for the cube of a binomial.

Hence, x^3 - 9x^2 + 27x - 27 can be written as: (x - 3)^3.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.