Question

1)25a²-c², 2)x²-4y², 3)27a³-64b³, 4)a³-a²b+ab²-b3, 5)3b+bc+3ac+9a, 6)c²-6c+9-4x², 7)y²x+y+yx²+x+4yx+4.

Answer 1

Помогите Алгебра (Разложение на множители)
1) 25a^2 - c^2 
2) 9x^2 - 16y^2 
3) x^2 - 4y^2 
4) x^3 - 8y^3 
5) 27a^3 - 64b^3 
6) 8x^3 - 125y^3 
7) a^3 - a^2 b + ab^2 - b^3 
8) x^2 - b^2 - ax -ab 
9) 3b + bc + 3ac + 9a 
10) a^2 x^2 - y^4 
11) a^2 y^2 - x^6 
12) c^2 - 4c + 4 - 9x^2 
13) c^2 - 6c + 9 -4x^2 
14) 4c^2 + 20c + 25 - 9a^2 
15) y^2 x + y + y x^2 + x + 4yx +4 
16) 3x^2 + 2x - xy - 2y^2 + y^3 - 3xy^2 
17) x^2 + x - xy - y^2 + y^3 - xy^2 
18) a^2 x + a +a x^2 + x + 2ax + 21) 25a^2 - c^2 = (5a+c)(5a-c)
2) 9x^2 - 16y^2 = (3x-4y)(3x+4y)
3) x^2 - 4y^2 = (x-2y)(x+2y)
4) x^3 - 8y^3 =(x-2y)(x^2+4y^2+2xy)
5) 27a^3 - 64b^3 =(3a-4b)(9a^2+16b^2+12ab)
6) 8x^3 - 125y^3 =(2x-5y)(4x^2+25y^2+10xy)
7) a^3 - a^2 b + ab^2 - b^3 =a^2(a-b)+b^2(a-b)=(a^2+b^2)(a-b)
8) x^2 - b^2 - ax -ab =(x-b)(x+b)-a(x+b)=(x+b)(x-b-a)
9) 3b + bc + 3ac + 9a = b(3+c)+3a(c+3)=(3+c)(3a+b)
10) a^2 x^2 - y^4 =(ax-y^2)(ax+y^2)
11) a^2 y^2 - x^6 =(ay-x^3)(ay+x^3)
12) c^2 - 4c + 4 - 9x^2 
13) c^2 - 6c + 9 -4x^2 =(c-3)^2-4x^2=(c-3-2x)(x-3+2x)
14) 4c^2 + 20c + 25 - 9a^2= (2c+5)^2-9a^2=(2c+5-3a)(2c+5+3a)
15) y^2 x + y + y x^2 + x + 4yx +4 
16) 3x^2 + 2x - xy - 2y^2 + y^3 - 3xy^2 
17) x^2 + x - xy - y^2 + y^3 - xy^2 
18) a^2 x + a +a x^2 + x + 2ax + 2=

Answer 2

1) 25a² - c²: To simplify this expression, we can use the difference of squares formula, which states that a² - b² can be factored as (a + b)(a - b). Applying this formula to 25a² - c², we have:

25a² - c² = (5a)² - c² = (5a + c)(5a - c)

So, the expression 25a² - c² can be factored as (5a + c)(5a - c).

2) x² - 4y²: The expression x² - 4y² is a difference of squares as well. It can be factored using the same formula:

x² - 4y² = (x)² - (2y)² = (x + 2y)(x - 2y)

Therefore, x² - 4y² can be factored as (x + 2y)(x - 2y).

3) 27a³ - 64b³: This expression is a difference of cubes. The formula for factoring a³ - b³ is (a - b)(a² + ab + b²). Applying this formula to 27a³ - 64b³, we get:

27a³ - 64b³ = (3a)³ - (4b)³ = (3a - 4b)(9a² + 12ab + 16b²)

Thus, 27a³ - 64b³ can be factored as (3a - 4b)(9a² + 12ab + 16b²).

4) a³ - a²b + ab² - b³: This expression does not appear to have a simple factorization using standard formulas. It is already in its simplest form.

5) 3b + bc + 3ac + 9a: This expression does not appear to be factorable. It is already in its simplest form.

6) c² - 6c + 9 - 4x²: This expression can be simplified by factoring it as a difference of squares:

c² - 6c + 9 - 4x² = (c - 3)² - (2x)² = (c - 3 + 2x)(c - 3 - 2x)

So, c² - 6c + 9 - 4x² can be factored as (c - 3 + 2x)(c - 3 - 2x).

7) y²x + y + yx² + x + 4yx + 4: This expression does not appear to be factorable. It is already in its simplest form.

In summary, the factorizations of the given expressions are: 1) 25a² - c² = (5a + c)(5a - c) 2) x² - 4y² = (x + 2y)(x - 2y) 3) 27a³ - 64b³ = (3a - 4b)(9a² + 12ab + 16b²) 4) a³ - a²b + ab² - b³ = a³ - a²b + ab² - b³ (no further factorization) 5) 3b + bc + 3ac + 9a = 3b + bc + 3ac + 9a (no further factorization) 6) c² - 6c + 9 - 4x² = (c - 3 + 2x)(c - 3 - 2x) 7) y²x + y + yx² + x + 4yx + 4 = y²x + y + yx² + x + 4yx + 4 (no further factorization)