40:

a: =(xy+1+x+y)(xy+1-x-y)

=[x(y+1)+(y+1)][x(y-1)-(y-1)]

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

b: =(a+b)^2+2c(a+b)+c^2+(a+b)^2-2c(a+b)+c^2-4c^2

=2(a+b)^2-2c^2

=2[(a+b)^2-c^2]

=2(a+b+c)(a+b-c)

c: =(2ab-a^2-b^2+c^2)(2ab+a^2+b^2-c^2)

=[c^2-(a-b)^2][(a+b)^2-c^2]

=(c-a+b)(c+a-b)(a+b-c)(a+b+c)

a)x²-6x+9

=x²-2.x.3+3²

=(x-3)²

b)4x²+4x+1

=(2x)²+2.2x.1+1²

=(2x+1)²

c)4x²+12xy+9y²

=(2x)²+2.2x.3y+(3y)²

=(2x+3y)²

d)4x⁴-4x²+4

=(2x²)²-2.2x².2+2²

=(2x²-2)²

\(11x^2-5x-34=11x^2-22x+17x-34=11x\left(x-2\right)+17\left(x-2\right)=\left(x-2\right)\left(11x+17\right)\)

y²(\(x\)  + y) - ( \(x\) - 7)² (đk \(x\) +y ≥ 0)

= (y\(\sqrt{\left(x+y\right)}\) )² - (\(x\) - 7)²

= (y\(\sqrt{x+y}\) - (\(x-7\)))( y\(\sqrt{x+y}\) + (\(x\) - 7))

= (y\(\sqrt{x+y}\) - \(x\) + 7)(y\(\sqrt{x+y}\) + \(x\) - 7)

a) Ta có:

VT = (x - y)² + 4xy

= x² - 2xy + y² + 4xy

= x² + 2xy + y²

= (x + y)²

= VP

b) Ta có:

(x + y)² = (x - y)² + 4xy

= 5² + 4.3

= 25 + 12

= 37

a : 7 dư 3 cm a² : 7 dư 2

Ta có:     a = 7k + 3

          ⇔ a² = (7k + 3)²

          ⇔ a² = 49k² + 42k + 9

          ⇔ a² = 7.(7k² + 6k + 1) + 2

                7 ⋮ 7 ⇔ 7.(7k² + 6k + 1) ⋮ 7

          ⇔ a² = 7.(7k² + 6k + 1) + 2 : 7 dư 2 (đpcm)

Cách 2 sử dụng đồng dư thức:

a \(\equiv\) 3 (mod 7) ⇔ a² \(\equiv\) 3² (mod 7)  3² : 7 dư 2 ⇔ a² : 7 dư 2 (đpcm)

\(\text{∘ Ans}\)

\(\downarrow\)

`1,`

`86.15 + 150. 1,4`

`= 86. 15 + 15. 14`

`= 15.(86 + 14)`

`= 15.100`

`= 1500`

`2,`

`93.32 + 14.16`

`= 93.32 + 2.7.16`

`= 93.32 + 32.7`

`= 32.(93 + 7)`

`= 32.100`

`= 3200`

`3,`

\(98,6\cdot199-990\cdot9,86\)

`=`\(98,6\cdot199-99\cdot98,6\)

`=`\(98,6\cdot\left(199-99\right)\)

`=`\(98,6\cdot100\)

`=`\(9860\)

`4,`

\(85\cdot12,7+5\cdot3\cdot12,7?\)

`=`\(85\cdot12,7+15+12,7\)

`=`\(12,7\cdot\left(85+15\right)\)

`=`\(12,7\cdot100\)

`= 1270`

`5,`

\(0,12\cdot90-110\cdot0,6+36-25\cdot6?\)

\(=6\cdot1,8-11\cdot6+6\cdot6-25\cdot6\)

\(=6\cdot\left(1,8-11+6-25\right)\)

\(=6\cdot\left(-28,2\right)=-169,2\)