Question

№ 1 . Разложить на множители (представьте в виде произведения двучленов). a2 – 9 4 – y2 9x2 – 4 9a2 – 16m2 b2 + 1 9 – b4 48m2 – n2 36m6 – 49k4n2 № 2 Выполнить умножение (произведение разности и суммы двух выражений. ПРИМЕР: (a-b)(a+b)=a²+ab-ab-b²=a²-b²). (x –y)(x +y) (2x – 1)(2x+1) (8c + 9d)(8c – 9d) (1 – 3k)(1 +3k) (a2-3)(a2+3) (y-a2)(y+a2) (b3-c)(b3 +c) (m2-p3)(m2+p3)

Answer 1

Ответ:

(a-3)(a+3)

(2-y)(2+y)

(3x-2)(3x+2)

(3a _4m)(3a+4m)

(b+1)(b-1)

(3-b в квадрате) (3+b в квадрате)

(7m-n)(7m+n)

(6m3-7k2n)(6m3+7k2n)

Номер 2

X2-y2

4x2-1

64c2-81d2

1-9k2

A4-9

Y2-a4

B6-c2

M4-p6

Answer 2

№ 1. Разложение на множители:

a^2 – 9 This expression is a difference of squares, which can be factored as (a + 3)(a - 3).

4 – y^2 This expression is also a difference of squares, which can be factored as (2 - y)(2 + y).

9x^2 – 4 This expression is a difference of squares and can be factored as (3x - 2)(3x + 2).

9a^2 – 16m^2 This expression is a difference of squares and can be factored as (3a - 4m)(3a + 4m).

b^2 + 1 This expression cannot be factored further since it is a sum of squares.

9 – b^4 This expression can be factored as (3 - b^2)(3 + b^2). However, (3 + b^2) is a sum of squares and cannot be factored further.

48m^2 – n^2 This expression is a difference of squares and can be factored as (6m - n)(6m + n).

36m^6 – 49k^4n^2 This expression is a difference of squares and can be factored as (6m^3 - 7k^2n)(6m^3 + 7k^2n).

№ 2. Произведение разности и суммы двух выражений:

(x – y)(x + y) = x^2 - y^2

(2x – 1)(2x + 1) = (2x)^2 - 1^2 = 4x^2 - 1

(8c + 9d)(8c – 9d) = (8c)^2 - (9d)^2 = 64c^2 - 81d^2

(1 – 3k)(1 + 3k) = 1^2 - (3k)^2 = 1 - 9k^2

(a^2 - 3)(a^2 + 3) = a^4 - 3^2 = a^4 - 9

(y - a^2)(y + a^2) = y^2 - (a^2)^2 = y^2 - a^4

(b^3 - c)(b^3 + c) = (b^3)^2 - c^2 = b^6 - c^2

(m^2 - p^3)(m^2 + p^3) = (m^2)^2 - (p^3)^2 = m^4 - p^6