a: Khi x=2 và y=-3 thì \(x^2+2y=2^2+2\cdot\left(-3\right)=4-6=-2\)

b: \(A=x^2+2xy+y^2=\left(x+y\right)^2\)

Khi x=4 và y=6 thì \(A=\left(4+6\right)^2=10^2=100\)

c: \(P=x^2-4xy+4y^2=\left(x-2y\right)^2\)

Khi x=1 và y=1/2 thì \(P=\left(1-2\cdot\dfrac{1}{2}\right)^2=\left(1-1\right)^2=0\)

20

Ta có : `x^2+2xy+y^2=(x+y)^2`

Tại `x=4;y=3` ta có : `(x+y)^2 =(4+3)^2=7^2=49`

\(x^2+2xy+y^2-2x-2y=\left(x+y\right)^2-2\left(x+y\right)=\left(-6\right)^2-2.\left(-6\right)=\)

Ta có: \(x^2-2xy-4z^2+y^2\)

\(=\left(x^2-2xy+y^2\right)-4z^2\)

\(=\left(x-y\right)^2-4z^2=\left(x-y-2z\right)\left(x-y+2z\right)\)

\(=\left[6-\left(-4\right)-2\cdot45\right]\left[6-\left(-4\right)+2\cdot45\right]=-80\cdot100=-8000\)

x² - 2xy + y² - 4z²

= (x - y)² - (2z)²

= (x - y - 2z) (x - y + 2z)

Thay x = 6 ; y = -4 và z = 45 vào biểu thức ta được:

[6 - (-4) - 2 . 45] [6 - (-4) + 2 . 45]

= -80 . 100

= -8000

(x³ - 4y)(x² - 2xy + 4y)(x² + 2xy + 4y) tại x = -2; y = 1/2

Thay x = -2; y = 1/2 vào biểu thức, ta có:

[(-2)³ - 4.(1/2)].[(-2)² - 2.(-2).(1/2) + 4.(1/2)].[(-2)² + 2.(-2).(1/2) + 4.(1/2)]

= -10.8.4

= -320

Vậy:..

5A:

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

c: \(y^2-4x^2+4x-1=y^2-\left(2x-1\right)^2\)

=(y-2x+1)(y+2x-1)

b: \(x^2-y^2-5y+5x\)

=(x-y)(x+y)+5(x-y)

=(x-y)(x+y+5)

6A:

a: \(x^2-8x+7\)

\(=x^2-x-7x+7\)

=x(x-1)-7(x-1)

=(x-1)(x-7)

b: \(2x^2-5x+2\)

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

=2x(x-2)-(x-2)

=(x-2)(2x-1)

c: \(x^3-5x^2+8x-4\)

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

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

\(a,=5\left(x^2+2xy+y^2\right)-10y^2+5=5\left(x+y\right)^2-10y^2+5\\ =5\left(1+2\right)^2-10\cdot4+5=45-40+5=10\\ b,=7\left(x-y\right)-\left(x-y\right)^2=\left(x-y\right)\left(7-x+y\right)\\ =\left(2-2\right)\left(7-2+2\right)=0\)

b: \(=7\left(x-y\right)-\left(x-y\right)^2\)

\(=\left(x-y\right)\left(7-x+y\right)=0\)