Задание 381

Решение:

• \({\largeа)}\ a^2-b^2=(a+b)(a-b)\)

• \({\largeб)}\ y^2-x^2=(y+x)(y-x)\)

• \({\largeв)}\ (2x)^2-1=(2x+1)(2x-1)\)

• \({\largeг)}\ 9-(3m)^2=3^2-(3m)^2=(3+3m)(3-3m)=3(1+m)\cdot3(1-m)=9(1+m)(1-m)\)

• \({\largeд)}\ 16-p^4=4^2-(p^2)^2=(4+p^2)(4-p^2)=(4+p^2)(2^2-p^2)=(4+p^2)(2+p)(2-p)\)

• \({\largeе)}\ 25-a^6=5^2-(a^3)^2=(5+a^3)(5-a^3)\)

• \({\largeж)}\ m^4-n^2=(m^2)^2-n^2=(m^2+n)(m^2-n)\)

• \({\largeз)}\ p^8-49=(p^4)^2-7^2=(p^4+7)(p^4-7)\)

• \({\largeи)}\ 1-x^4=1^2-(x^2)^2=(1+x^2)(1-x^2)=(1+x^2)(1^2-x^2)=(1+x^2)(1+x)(1-x)\)

• \({\largeк)}\ a^4-b^4=(a^2)^2-(b^2)^2=(a^2+b^2)(a^2-b^2)=(a^2+b^2)(a+b)(a-b)\)