Question

Помогите пожалуйста!!! Разложить на множители :1) 25x^2-16 2) 49a^4-4b^6 3) 9x^2-12xy+4y2 4) x^3-64xy^2 5) -7a^2-14ab-7b^2 6) m^3+27n^3

Answer 1

1) (5х-4)(5х+4)

2)(7a^2-2b^3)(7a^2+2b^3)

3)(3x-2y)^2

4)x(x^2-64y^2)=x(x-8y)(x+8y)

5)-7(a+b)^2

6)(m+3n)(m^2-3mn+9n^2)

Answer 2

1. 25x^2 - 16 can be factored as the difference of two squares:

25x^2 - 16 = (5x)^2 - 4^2 = (5x + 4)(5x - 4)

2. 49a^4 - 4b^6 can also be factored as the difference of two squares:

49a^4 - 4b^6 = (7a^2)^2 - (2b^3)^2 = (7a^2 + 2b^3)(7a^2 - 2b^3)

3. 9x^2 - 12xy + 4y^2 can be factored as a perfect square:

9x^2 - 12xy + 4y^2 = (3x - 2y)^2

4. x^3 - 64xy^2 can be factored as the difference of two cubes:

x^3 - 64xy^2 = (x - 4y)(x^2 + 4xy + 16y^2)

5. -7a^2 - 14ab - 7b^2 can be factored by factoring out the common factor of -7:

-7a^2 - 14ab - 7b^2 = -7(a^2 + 2ab + b^2) = -7(a + b)^2

6. m^3 + 27n^3 can be factored as the sum of two cubes:

m^3 + 27n^3 = (m + 3n)(m^2 - 3mn + 9n^2)