Задание 345

Решение:

• $${\largeа)}\ x^2+2xy+y^2=(x+y)^2$$

• $${\largeб)}\ a^2+4ab+4b^2=a^2+2\cdot{a}\cdot2b+(2b)^2=(a+2b)^2$$

• $${\largeв)}\ 9m^2+6mn+n^2=(3m)^2+2\cdot3m\cdot{n}+n^2=(3m+n)^2$$

• $${\largeг)}\ 16p^2+40pq+25q^2=(4p)^2+2\cdot4p\cdot5q+(5q)^2=(4p+5q)^2$$

• $${\largeд)}\ x^2+2x+1=(x+1)^2$$

• $${\largeе)}\ 9+6a+a^2=3^2+2\cdot3\cdot{a}+a^2=(3+a)^2$$

• $${\largeж)}\ 16+8p+p^2=4^2+2\cdot4\cdot{p}+p^2=(4+p)^2$$

• $${\largeз)}\ 4m^2+9n^2+12mn=4m^2+12mn+9n^2=(2m)^2+2\cdot2m\cdot3n+(3n)^2=(2m+3n)^2$$

• $${\largeи)}\ x^4+2x^2y^3+y^6=(x^2)^2+2\cdot{x^2}\cdot{y^3}+(y^3)^2=(x^2+y^3)^2$$

• $${\largeк)}\ a^6+2a^3b^3+b^6=(a^3)^2+2\cdot{a^3}\cdot{b^3}+(b^3)^2=(a^3+b^3)^2$$