Задание 407

Решение:

• \({\largeа)}\ (x-y)(x^2+xy+y^2)=x^3-y^3\)

• \({\largeб)}\ (5-a)(a^2+5a+25)=(5-a)(25+5a+a^2)=5^3-a^3=125-a^3\)

• \({\largeв)}\ (2m-5n)(4m^2+10mn+25n^2)=(2m)^3-(5n)^3=8m^3-125n^3\)

• \({\largeг)}\ (7p+q)(49p^2-7pq+q^2)=(7p)^3+q^3=343p^3+q^3\)

• \({\largeд)}\ \left(\frac{1}{2}x-\frac{1}{3}y\right)\left(\frac{1}{4}x^2+\frac{1}{6}xy+\frac{1}{9}y^2\right)=\left(\frac{1}{2}x\right)^3-\left(\frac{1}{3}y\right)^3=\frac{1}{8}x^3-\frac{1}{27}y^3\)

• \({\largeе)}\ (0{,}1a-0{,}2b)(0{,}04b^2+0{,}02ab+0{,}01a^2)=(0{,}1a-0{,}2b)(0{,}01a^2+0{,}02ab+0{,}04b^2)=(0{,}1a)^3-(0{,}2b)^3=0{,}001a^3-0{,}008b^3\)