Question

em cần gấp ạ

Answer 1

Bài 2:

a: \(x^2-9\left(a-b\right)^2\)

\(=x^2-\left(3a-3b\right)^2\)

=(x-3a+3b)(x+3a-3b)

b: \(\frac14\left(x+y\right)^2-1\)

\(=\left(\frac12x+\frac12y\right)^2-1=\left(\frac12x+\frac12y-1\right)\left(\frac12x+\frac12y+1\right)\)

c: \(\frac{25}{49}\left(x+y\right)^2-4\left(x-y\right)^2\)

\(=\left(\frac57x+\frac57y\right)^2-\left(2x-2y\right)^2\)

\(=\left(\frac57x+\frac57y-2x+2y\right)\left(\frac57x+\frac57y+2x-2y\right)\)

\(=\left(-\frac97x+\frac{19}{7}y\right)\left(\frac{19}{7}x-\frac97y\right)\)

d: \(x^3y^2+18x^2y^2+108xy^2+216y^2\)

\(=y^2\left(x^3+18x^2+108x+216\right)=y^2\left(x+6\right)^3\)

e: \(\frac18a^3b^9+64x^3=\left(\frac12ab^3\right)^3+\left(4x\right)^3\)

\(=\left(\frac12ab^3+4x\right)\left(\frac14a^2b^6-\frac12ab^3\cdot4x+16x^2\right)\)

\(=\left(\frac12ab^3+4x\right)\left(\frac14a^2b^6-2ab^3x+16x^2\right)\)

g: \(-\frac{1}{125}a^3-\frac18x^3y^3\)

\(=-\left\lbrack\left(\frac15a\right)^3+\left(\frac12xy\right)^3\right\rbrack\)

\(=-\left(\frac15a+\frac12xy\right)\left(\frac{1}{25}a^2-\frac{1}{10}a\cdot xy+\frac14x^2y^2\right)\)

Bài 3:

a: \(x^3-4x^2-9x+36=0\)

=>\(x^2\cdot\left(x-4\right)-9\left(x-4\right)=0\)

=>\(\left(x-4\right)\left(x^2-9\right)=0\)

=>(x-4)(x-3)(x+3)=0

=>\(\left[\begin{array}{l}x-4=0\\ x-3=0\\ x+3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=4\\ x=3\\ x=-3\end{array}\right.\)

b: \(2x^3-4x=0\)

=>\(2x\left(x^2-2\right)=0\)

=>\(x\left(x^2-2\right)=0\)

=>\(\left[\begin{array}{l}x=0\\ x^2-2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=\sqrt2\\ x=-\sqrt2\end{array}\right.\)

c: \(x^2-4x-1=0\)

=>\(x^2-4x+4-5=0\)

=>\(\left(x-2\right)^2=5\)

=>\(\left[\begin{array}{l}x-2=\sqrt5\\ x-2=-\sqrt5\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\sqrt5+2\\ x=-\sqrt5+2\end{array}\right.\)