Question

Розложить на множители 49с^2-(2c-15)^2 9(5a-4b)^2-64a^2 (1+x)^3-27x^3 x^2-4xy+4н: 2+2х-4у выражение ( (а^2-3a)^3-a^2(a+2)(a-2)+2a(3a^2+7)

Answer 1

$49c^2-(2c-15)^2=49c^2-(4c^2-60c+225)= \\ =49c^2-4c^2+60c-225=45c^2+60c-225= \\ =5(9c^2+12c-45)=5(x+3)(3x-5)$

$9(5a-4b)^2-64a^2=9(25a^2-40ab+16b^2)-64a^2= \\ =225a^2-360ab+144b^2-64a^2=161a^2-360ab+144b^2= \\ =161a^2-84ab-276ab+144b^2=7a(23a-12b)-12b(23a-12b)= \\ =(7a-12b)(23a-12b)$

$(1+x)^3-27x^3=1+3x+3x^2+x^3-27x^3= \\ =1+3x+3x^2-26x^3=1+3x+3x^2-26x^3= \\ =1+5x-2x+13x^2-10x^2-26x^3= \\ =(1+5x+13x^2)-2x(1+5x+13x^2)= \\ =(1-2x)(1+5x+13x^2)$

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

$(a^2-3a)^3-a^2(a+2)(a-2)+2a(3a^2+7)= \\ =(a^2-3a)^3-a^2(a^2-4)+2a(3a^2+7)= \\ =(a^6-9a^5+27a^4-27a^3)-(a^4-4a^2)+(6a^3+14a)= \\ =a^6-9a^5+27a^4-27a^3-a^4+4a^2+6a^3+14a= \\ =a^6-9a^5+26a^4-21a^3+4a^2+14a= \\ =a(a^5-9a^4+26a^3-21a^2+4a+14)$