Задание 339

Решение:

• \({\largeа)}\ (m+n)^2=(m+n)(m+n)=m^2+mn+mn+n^2=m^2+2mn+n^2\)

• \(\phantom{\largeа)}\ (m+n)^2=m^2+2mn+n^2\)

• \({\largeб)}\ (2+x)^2=(2+x)(2+x)=4+2x+2x+x^2=4+4x+x^2\)

• \(\phantom{\largeб)}\ (2+x)^2=2^2+2\cdot2x+x^2=4+4x+x^2\)

• \({\largeв)}\ (y+4)^2=(y+4)(y+4)=y^2+4y+4y+16=y^2+8y+16\)

• \(\phantom{\largeв)}\ (y+4)^2=y^2+2\cdot4y+4^2=y^2+8y+16\)

• \({\largeг)}\ (1+p)^2=(1+p)(1+p)=1+p+p+p^2=1+2p+p^2\)

• \(\phantom{\largeг)}\ (1+p)^2=1^2+2\cdot1\cdot{p}+p^2=1+2p+p^2\)

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

• \(\phantom{\largeд)}\ (2x+1)^2=(2x)^2+2\cdot2x\cdot1+1^2=4x^2+4x+1\)

• \({\largeе)}\ (2+3a)^2=(2+3a)(2+3a)=4+6a+6a+9a^2=4+12a+9a^2\)

• \(\phantom{\largeе)}\ (2+3a)^2=2^2+2\cdot2\cdot3a+(3a)^2=4+12a+9a^2\)

• \({\largeж)}\ (2m+5n)^2=(2m+5n)(2m+5n)=4m^2+10mn+10mn+25n^2=4m^2+20mn+25n^2\)

• \(\phantom{\largeж)}\ (2m+5n)^2=(2m)^2+2\cdot2m\cdot5n+(5n)^2=4m^2+20mn+25n^2\)

• \({\largeз)}\ (3x+4y)^2=(3x+4y)(3x+4y)=9x^2+12xy+12xy+16y^2=9x^2+24xy+16y^2\)

• \(\phantom{\largeз)}\ (3x+4y)^2=(3x)^2+2\cdot3x\cdot4y+(4y)^2=9x^2+24xy+16y^2\)