Question

Разложить на множители (представьте в виде произведения двучленов). 1) x6 – 1,44 2) y12 – 16 3) 4x2y4 – 9 4) 9a2b2 – 64x4 5) 1,21p2 – a6 6) 100x4 – 9y10 7) 0,04a6 – 0,25b4 8) 0,09x6 – 0,49y2 9) x10 – y8 10) 1,69y14 – 1,21 11) 121m8n8 – 9

Answer 1

1) $x^6 - 1,44 = (x^3)^2 - (1,2)^2 = (x^3 - 1,2)(x^3+1,2)$

2) $y^{12} - 16 = (y^6)^2 - 4^2 = ( y^6 - 4)( y^6 +4) = ((y^3)^2-2^2)(y^6 +4) = \\ \\ = (y^3 -2)(y^3 +2)(y^6 +4)$

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

4) $9a^2b^2 - 64x^4 = (3ab)^2 - (8x^2)^2 = (3ab -8x^2)(3ab +8x^2)$

5) $1,21p^2 - a^6 = (1,1p)^2 - (a^3)^2 = (1,1p - a^3)(1,1p + a^3)$

6) $100x^4 - 9y^{10} = (10x^2)^2 -(3y^5)^2 = (10x^2-3y^5)(10x^2+3y^5)$

7) $0,04a6 - 0,25b4 = (0,2a^3)^2 - (0,5b^2)^2 = \\ \\ =(0,2a^3-0,5b^2)(0,2a^3+ 0,5b^2)$

8) $0,09x^6 - 0,49y^2 = (0,3x^3)^2 - (0,7y)^2 = (0,3x^3 -0,7y)(0,3x^3 +0,7y)$

9) $x^{10} - y^8 = (x^5)^2 -(y^4)^2 = (x^5 -y^4) (x^5 +y^4)$

10) $1,69y^{14} - 1,21 = (1,3y^7)^2 -1,1^2 = (1,3y^7 -1,1)(1,3y^7 +1,1)$

11) $121m^8n^8 - 9 = (11m^4n^4)^2 -3^2 = (11m^4n^4 -3)(11m^4n^4 +3)$

Answer 2

1) x^6 - 1.44 can be factored as (x^3 - 1.2)(x^3 + 1.2).

2) y^12 - 16 can be factored as (y^6 - 4)(y^6 + 4).

3) 4x^2y^4 - 9 can be factored as (2xy^2 - 3)(2xy^2 + 3).

4) 9a^2b^2 - 64x^4 can be factored as (3ab - 8x^2)(3ab + 8x^2).

5) 1.21p^2 - a^6 can be factored as (1.1p - a^3)(1.1p + a^3).

6) 100x^4 - 9y^10 can be factored as (10x^2 - 3y^5)(10x^2 + 3y^5).

7) 0.04a^6 - 0.25b^4 can be factored as (0.2a^3 - 0.5b^2)(0.2a^3 + 0.5b^2).

8) 0.09x^6 - 0.49y^2 can be factored as (0.3x^3 - 0.7y)(0.3x^3 + 0.7y).

9) x^10 - y^8 can be factored as (x^5 - y^4)(x^5 + y^4).

10) 1.69y^14 - 1.21 can be factored as (1.3y^7 - 1)(1.3y^7 + 1).

11) 121m^8n^8 - 9 can be factored as (11m^4n^4 - 3)(11m^4n^4 + 3).