Bài 12:

a) \(\left(\dfrac{1}{2}x+4\right)^2\)

\(=\left(\dfrac{1}{2}x\right)^2+2\cdot\dfrac{1}{2}x\cdot4+4^2\)

\(=\dfrac{1}{4}x^2+4x+16\)

b) \(\left(7x-5y\right)^2\)

\(=\left(7x\right)^2-2\cdot7x\cdot5y+\left(5y\right)^2\)

\(=49x^2-70xy+25y^2\)

c) \(\left(6x^2+y^2\right)\left(y^2-6x^2\right)\)

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

\(=y^4-36x^4\)

d) \(\left(x+2y\right)^2\)

\(=x^2+2\cdot x\cdot2y+\left(2y\right)^2\)

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

e) \(\left(x-3y\right)\left(x+3y\right)\)

\(=x^2-\left(3y\right)^2\)

\(=x^2-9y^2\)

f) \(\left(5-x\right)^2\)

\(=5^2-2\cdot5\cdot x+x^2\)

\(=25-10x+x^2\)

\(11,\)

\(a,\left(7x+4\right)^2-\left(7x+4\right)\left(7x-4\right)\)

\(=\left(7x+4\right)\left(7x+4-7x+4\right)\)

\(=\left(7x+4\right).8=56x+32\)

\(b,\left(x+2y\right)^2-6xy\left(x+2y\right)\)

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

Bài `12`

`(1/2x+4)^2`

`=(1/2x)^2 + 2 . 1/2x.4 + 4^2`

`= 1/4 x^2 +4x + 16`

__

`(7x-5y)^2`

`=(7x)^2-2.7x.5y+(5y)^2`

`= 49x^2 -  70xy   + 25y^2`

__

`(6x^2+y^2)(y^2-6x^2)`

`=(y^2+6x^2)(y^2-6x^2)`

`=(y^2)^2 - (6x^2)^2`

`=y^4-36x^4`

__

`(x+2y)^2`

`=x^2+ 2.x.2y+(2y)^2`

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

__

`(x-3y)(x+3y)`

`=x^2 - (3y)^2`

`=x^2 - 9y^2`

__

`(5-x)^2`

`=5^2 -2.5.x+x^2`

`=25 - 10x+x^2`

Bài `11`

`(7x+4)^2 -(7x+4)(7x-4)`

`= (7x+4)(7x+4) -(7x+4)(7x-4)`

`=(7x+4)(7x+4-7x+4)`

`=8(7x+4)`

`= 56x+32`

__

`(x+2y)^2-6xy (x+2y)`

`= (x+2y) (x+2y-6xy)`

a) \(3x^2-2x\left(5+1,5x\right)+10x\)

\(=3x^2-10x-3x^2+10x=0\)

b) \(7x\left(4y-x\right)+4y\left(y-7x\right)-2\left(2y^2-3,5x\right)\)

\(=28xy-7x^2+4y^2-28xy-4y^2+7x\)

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

a: Ta có: \(x^2-4x\left(3x-4\right)+7x-5\)

\(=x^2-12x^2+16x+7x-5\)

\(=-11x^2+23x-5\)

b: Ta có: \(7x\left(x^2-5\right)-3x^2y\left(xy-6y^2\right)\)

\(=7x^3-35x-3x^3y^2+18x^2y^3\)

c: Ta có: \(\left(5x+4\right)\left(2x-7\right)\)

\(=10x^2-35x+8x-28\)

\(=10x^2-27x-28\)

 x ≤ 0 nên – 3x ≥ 0 ⇒ |-3x| = -3x

Vậy C = |-3x| + 7x – 4 = -3x + 7x - 4 = 4x - 4

Với \(x\ne1\)ta có 

\(P=\left(\frac{4}{x-1}-\frac{7x+5}{x^3-1}\right):\left(1-\frac{x-4}{x^2+x+1}\right)\)

\(=\left[\frac{4x^2+4x+4-7x-5}{\left(x-1\right)\left(x^2+x+1\right)}\right]:\left(\frac{x^2+x+1-x-4}{x^2+x+1}\right)\)

\(=\frac{4x^2-3x-1}{\left(x-1\right)\left(x^2+x+1\right)}:\frac{x^2-3}{x^2+x+1}=\frac{4x+1}{x^2-3}\)

a: =12x^4-6x^3+3x+4x^3-2x^2+1

=12x^4-2x^3-2x^2+3x+1

b: =14x^4+28x^2+6x^2+12x

=14x^4+34x^2+12x

`@` `\text {Ans}`

`\downarrow`

\((3x + 1)(4x³ - 2x² + 1)\)

`= 3x(4x^3-2x^2+1) + 4x^3 - 2x^2 + 1`

`= 12x^4 - 6x^3 + 3x + 4x^3 - 2x^2 + 1`

`= 12x^4 + (-6x^3 + 4x^3) - 2x^2 + 3x + 1`

`= 12x^4 - 2x^3 - 2x^2 + 3x + 1`

\((7x² + 3x)(2x + 4)\)

`= 7x^2(2x+4) + 3x(2x+4)`

`= 14x^3 + 28x^2 + 6x^2 + 12x`

`= 14x^3 + (28x^2 + 6x^2)+12x`

`= 14x^3 + 34x^2 + 12x`

`@` `\text {Kaizuu lv uuu}`

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

\(=x\left(x^2-16\right)\)

\(=x^3-16x-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x^3-16x-x^4+1\)

b) \(7x\left(4y-x\right)+4y\left(y-7x\right)-2\left(2y^2-3.5x\right)\)

\(=28xy-7x^2+4y\left(y-7x\right)-2\left(2y^2-3.5x\right)\)

\(=28xy-7x^2+4y^2-28xy-4y^2+7x\)

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

c) \(\left(3x-1\right)\left(2x-5\right)-4\left(2x^2-5x+2\right)\)

\(=6x^2-17x+5-4\left(2x^2-5x+2\right)\)

\(=6x^2-17x+5-8x^2+20x-8\)

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

a)  x(x+4)(x-4)-(x²+1)(x²-1)

=>x(x²-4²)-(x⁴-1²)

=>x³-16x-x⁴+1

=>-x⁴-x³-15x

b)  7x(4y-x)+4y(y-7x)-2(2y²-3.5x)

=>28xy-7x²+4y²-28xy-4y²+30x

=>-7x²+30x

c)  (3x+1)(2x-5)-4(2x²-5x+2)

=>6x²-15x+2x-5-8x²+20x-8

=>-2x²+7x-13