Question

Разложите на множители выражение:1) (5x-7)^2-(5-3x)^22) (a^2+6ab+16b^2)^2-(6ab+20b^2)^23) (4-6y^3+4y^6)^2-(6y^3-5y^6)^2Помогите,пожалуйста...

Answer 1

1) 16x²-40x+24

2) (a-2b)*(a+2b)*(a+6b)²

3) -9y¹²+12y⁹+32y⁶-48y³+16

Answer 2

(5x-7)^2-(5-3x)^2=$(5x-7+5-3x)(5x-7-5+3x)=(2x-2)(8x-12)$

(a^2+6ab+16b^2)^2-(6ab+20b^2)^2=$(a^{2}+6ab+16b^{2}+6ab+20b^{2})(a^{2}+6ab+16b^{2}-6ab-20b^{2})$=$(a^{2}+12ab+36b^{2})(a^{2}-4b^{2})$

(4-6y^3+4y^6)^2-(6y^3-5y^6)^2=$(4-6y^{3}+4y^{6}+6y^{3}-5y^{6})(4-6y^{3}+4y^{6}-6y^{3}+5y^{6})=(4-y^{6})(9y^{6}-12y^{3}+4)$

Answer 3

1) (5x-7)^2-(5-3x)^2 = (5x-7)^2 - (3x-5)^2 = (5x-7+3x-5)(5x-7-3x+5) = (8x-12)(2x-2) = 4(2x-3)(x-1)

2) (a^2+6ab+16b^2)^2-(6ab+20b^2)^2 = (a^2+6ab+16b^2+6ab+20b^2)(a^2+6ab+16b^2-6ab-20b^2) = (a^2+12ab+36b^2)(a^2) = (a+6b)^2(a-6b)^2

3) (4-6y^3+4y^6)^2-(6y^3-5y^6)^2 = (4-6y^3+4y^6+6y^3-5y^6)(4-6y^3+4y^6-6y^3+5y^6) = (4-5y^6)(4+y^6) = (2-y^3)(2+y^3)(2-y^2y^3)(2+y^2y^3)