Разложи ** множители (c+24d)2−(24c+d)2

Question

Разложи на множители (c+24d)2−(24c+d)2

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Answer 1

(c+24d)^2-(24c+d)^2=c^2+48cd+(24d)^2-(24c)^2-48cd-d^2=c^2-(24c)^2+(24d)^2-d^2=c^2(1-24^2)+d^2(24^2-1)=d^2 ×(24^2-1)-c^2(24^2-1)=(d^2-c^2)(24^2-1)=(d-c)(d+c)(24-1)(24+1)=23×25(d-c)(d+c)=575(d-c)(d+c)