a)\(7x+2=0\)

\(7x=-2\)

\(x=-\frac27\)

b)\(18-5x=7+3x\) \(\)

\(-8x=-11\)

\(x=\frac{11}{8}\)

225cm

\(a)x-3=(3-x)^2\)

\(\left(\right.x-3)-(3-x)^2=0\)

\(\left(\right.x-3)(3-x-1)=0\)

\(\rArr\left(\right.x-3)=0\) hoặc \((3-x-1)=0\)

\(\rArr x=3\) hoặc \(x=2\)

\(b)x^3+\frac32x^2+\frac34x+\frac18=\frac{1}{64}\)

\(\left(x+\frac12\right)^3=\left(\frac14\right)^3\)

\(x+\frac12=\frac14\)

\(\rArr x=-\frac14\)

\(a)x^2+2xy+y^2-x-y=\left(x^2+2xy+y^2)-\left(x+y\right)\right.=\left(x+y\right)^2-\left(x+y\right)=\left(x+y\right)\left(x+y-1\right)\)

\(b)2x^3+6x^2+12x+8=2\left(x^3+3x^2+6x=4\right)=2\left(x^3+x^2+2x^2+2x+4x+4\right)=2\left\lbrack\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(4x+4\right)\right\rbrack=2\left\lbrack x^2\left(x^{}+1\right)+2x\left(x^{}+1\right)+4\left(x+1\right)\right\rbrack=2\left(x+1\right)\left(x^2+2x+4\right)=\)

\(a)x^2+2xy+y^2-x-y=\left(x^2+2xy+y^2)-\left(x+y\right)\right.=\left(x+y\right)^2-\left(x+y\right)=\left(x+y\right)\left(x+y-1\right)\)

\(b)2x^3+6x^2+12x+8=2\left(x^3+3x^2+6x=4\right)=2\left(x^3+x^2+2x^2+2x+4x+4\right)=2\left\lbrack\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(4x+4\right)\right\rbrack=2\left\lbrack x^2\left(x^{}+1\right)+2x\left(x^{}+1\right)+4\left(x+1\right)\right\rbrack=2\left(x+1\right)\left(x^2+2x+4\right)=\)

a) Trong △ADC có MP // DC. Áp dụng định lí Thales. Ta có:

\(\frac{AM}{MD}=\frac{AP}{PC}\)

Trong △ABC có PN // AB. Áp dụng định lí Thales. Ta có:

\(\frac{BN}{NC}=\frac{AP}{PC}\)

Từ hai tỉ lệ thức trên, suy ra:

\(\frac{AM}{MD}=\frac{BN}{NC}\)

b) \(MP=2\operatorname{cm}\)

\(PN=\frac43cm\)

\(MN=\frac{10}{3}cm\)

a) Ta có:

\(3x(x−1)−1+x=0\)

\(3x\left(x-1)+\left(\right)1-x\right)=0\)

\(\left(x-1\right)\left(3x+1\right)=0\)

\(\rArr\left(x-1\right)=0\) hoặc \(\left(3x+1\right)=0\)

\(\rArr x=1\) hoặc \(x=-\frac13\)

b) Ta có:

\(x^2-9x=0\)

\(x\left(x-9\right)=0\)

\(\rArr x=0\) hoặc \(\left(x-9\right)=0\)

\(\rArr x=0\) hoặc \(x=9\)

\(a)x^2+25-10x=x^2-10x+25=\left(x-5\right)^2=\left(x-5\right)\left(x-5\right)\)\(\)

\(b)-8y^3+x^3=\left(-2y\right)^3+x^3=\left(-2y+x\right)\left(-4y^2-2xy+x^2\right)\)

a)  \(\left(2x+1\right)^2=4x^2+4x+1\)

b) \(\left(a-\frac{b}{2}\right)^3=a^3-\frac32a^2b+\frac34ab^2-\frac{b^3}{8}\)

1. H₂​SO_4​
2. 2NaOH
3. 2HCl
4. 2AgNO₃