Question

a,(x-1)^2 b,(1/2x-3y)^2 c,(2x^2-1)^2 d,(x-2y-1)^2

Answer 1

`a)(x-1)^2`

`=x^2-2*x*1+1^2`

`=x^2-2x+1`

`b)(1/2x-3y)^2`

`=(1/2x)^2-2*1/2x*3y+(3y)^2`

`=1/4x^2-3xy+9y^2`

`c)(2x^2-1)^2`

`=(2x^2)^2-2*2x^2*1+1^2`

`=4x^4-4x^2+1`

`d)(x-2y-1)^2`

`=(x-2y)^2-2*(x-2y)*1+1^2`

`=x^2-4xy+4y^2-2x+4y+1`

Answer 2

a: \(\left(x-1\right)^2=x^2-2x+1\)

b: \(\left(\dfrac{1}{2}x-3y\right)^2\)

\(=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot3y+\left(3y\right)^2\)

\(=\dfrac{1}{4}x^2-3xy+9y^2\)

c: \(\left(2x^2-1\right)^2\)

\(=\left(2x^2\right)^2-2\cdot2x^2\cdot1+1^2\)

\(=4x^4-4x^2+1\)

d: \(\left(x-2y-1\right)^2\)

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

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