ò ra vậy thank bạn

Bài 7:

a: \(\left(a^2-b^2\right)^2+2a^2b^2\)

\(=a^4+b^4-2a^2b^2+2a^2b^2\)

\(=a^4+b^4\)

b: \(\left(a^2+b^2\right)^3-3a^2b^2\left(a^2+b^2\right)\)

\(=a^6+b^6+3\cdot\left(a^2\right)^2\cdot b^2+3\cdot a^2\cdot\left(b^2\right)^2-3a^2b^4-3a^4b^2\)

\(=a^6+b^6+3a^4b^2+3a^2b^4-3a^4b^2-3a^2b^4\)

\(=a^6+b^6\)

c: \(\left(a+b+c\right)^2+a^2+b^2+c^2\)

\(=a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+c^2\)

\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(a^2+2ac+c^2\right)\)

\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(a+c\right)^2\)

Bài 6:

a: \(A=2x^2+3x-1\)

\(=2\left(x^2+\frac32x-\frac12\right)\)

\(=2\left(x^2+2\cdot x\cdot\frac34+\frac{9}{16}-\frac{9}{16}-\frac12\right)\)

\(=2\left\lbrack\left(x+\frac34\right)^2-\frac{9}{16}-\frac{8}{16}\right\rbrack=2\left(x+\frac34\right)^2-\frac{17}{8}\ge-\frac{17}{8}\forall x\)

Dấu '=' xảy ra khi \(x+\frac34=0\)

=>\(x=-\frac34\)

b: \(B=4x^2-x+1\)

\(=4\left(x^2-\frac14x+\frac14\right)\)

\(=4\left(x^2-2\cdot x\cdot\frac18+\frac{1}{64}+\frac{15}{64}\right)\)

\(=4\left(x-\frac18\right)^2+\frac{15}{16}\ge\frac{15}{16}\forall x\)

Dấu '=' xảy ra khi \(x-\frac18=0\)

=>\(x=\frac18\)

c: \(C=x^2+2y^2+2xy-4y+1\)

\(=x^2+2xy+y^2+y^2-4y+4-3\)

\(=\left(x+y\right)^2+\left(y-2\right)^2-3\ge-3\forall x,y\)

Dấu '=' xảy ra khi \(\begin{cases}x+y=0\\ y-2=0\end{cases}\Rightarrow\begin{cases}y=2\\ x=-y=-2\end{cases}\)

Bài 5:

a: \(3\left(x-1\right)^2+\left(2x+3\right)^2-7\left(x-2\right)\left(x+2\right)=2x-1\)

=>\(3\left(x^2-2x+1\right)+4x^2+12x+9-7\left(x^2-4\right)=2x-1\)

=>\(3x^2-6x+3+4x^2+12x+9-7x^2+28=2x-1\)

=>6x+40=2x-1

=>4x=-41

=>\(x=-\frac{41}{4}\)

b: \(\left(1-2x\right)^3+2x\left(2x-1\right)\left(2x+1\right)-3\left(3-2x\right)^2=2\)

=>\(1-6x+12x^2-8x^3+2x\left(4x^2-1\right)-3\left(4x^2-12x+9\right)=2\)

=>\(-8x^3+12x^2-6x+1+8x^3-2x-12x^2+36x-27=2\)

=>28x-26=2

=>28x=28

=>x=1

c: \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-19\)

=>\(x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-2x+1\right)=-19\)

=>\(x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-19\)

=>\(6x^2+2-6x^2+12x-6=-19\)

=>12x-4=-19

=>12x=-15

=>\(x=-\frac{15}{12}=-\frac54\)