Question

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

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