12
a
\(=\left(2x\right)^2+2.2x.3+3^2=4x^2+12x+9\)
b
\(=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=x^2-x+\dfrac{1}{4}\)
c
\(=\left(3x\right)^2-2.3x.2y+\left(2y\right)^2=9x^2-12xy+4y^2\)
d
\(=\left(x^2\right)^2+2.x^2.1+1^2=x^4+2x^2+1\)
13
a
\(=2\left(x^2+2x+1\right)-4\left(4-4x+x^2\right)+2x^2-6x\\ =2x^2+4x+2-16+16x-4x^2+2x^2-6x\\ =14x-14\)
b
\(=4\left(4x^2-4x+1\right)-\left(3x^2-2x+3x-2\right)\\ =16x^2-16x+4-3x^2+2x-3x+2\\ =13x^2-17x+6\)
13:
a: =2(x^2+2x+1)-4(x^2-4x+4)+2x^2-6x
=2x^2+4x+2+2x^2-6x-4(x^2-4x+4)
=4x^2-2x+2-4x^2+16x-16=14x-14
b: =4(4x^2-4x+1)-(3x^2-2x+3x-2)
=16x^2-16x+4-3x^2-x+2
=13x^2-17x+6
12:
a: (2x+3)^2=4x^2+12x+9
b: (x-1/2)^2=x^2-x+1/4
c: (3x-2y)^2=9x^2-12xy+4y^2
d: (x^2+1)^2=x^4+2x^2+1
