1) a) 978²+ 22²+ 978.44                                                                     b) 821² + 321² - 821.642

     = 978² + 22² + 2. 22. 978                                                                = 821² + 321²- 2. 321 .821

     = (978+22)²                                                                                         = ( 821 - 321)²

     = 1000²                                                                                                                       = 500²

     = 1 000 000                                                                                   = 250 000

2) (a+b+c)²+(a+b-c)²

   = a²+b²+ c² + 2ab +2ac+2bc+a²+b²-c²+ 2ab -2ac -2bc

  = 2a²+2b²+4ab

  = 2(a² + b² + 2ab)

 = 2( a+b)²

\(\left(a+b+c\right)^2+\left(a+b-c\right)^2\)

\(=\left(a^2+b^2+c^2+2ab+2bc+2ca\right)+\left(a^2+b^2+c^2+2ab-2bc-2ca\right)\)

\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2+2ab-2bc-2ca\)

\(=a^2+b^2+c^2+2ab+a^2+b^2+c^2+2ab\)

\(=2a^2+2b^2+2c^2+4ab\)

\(=2\left(a^2+b^2+c^2+2ab\right)\)

a)   \(978^2+22^2+978.22\)

\(=978^2+2.978.22+22^2\)

\(=\left(978+22\right)^2=1000^2=1000000\)

b)   \(821^2+321^2-821.642\)

\(=\left(821-321\right)^2=500^2=250000\)

\(821^2+321^2-821.642\)

\(=821^2+321^2-2.821.321\)

\(=\left(821-321\right)^2\) (Áp dụng hằng đẳng thức (a-b)²=a²-2ab+b²)

\(=500^2=250000\)

821² + 321² - 821 . 642

= 821² + 321² - 2.821.321

= (821 - 321)²

= 500²

= 250000.

\(812^2+321^2-821.642\)

\(=\left(812+321\right)\left(812+321\right)\)

\(=\left(812+321\right)^2\)

số số hạng là :`(26 - 2) : 2 + 1 = 13(số hạng)`

`13 : 2 = 12 dư 1 `

`=>A = (2 - 4) + (6 - 8) + (10 - 12) + ... + (22 - 24) + 26`

`=>A = (-2) + (-2) + (-2) + ... + (-2) + 26`

`=>A = (-2) xx 6 + 26`

`=> A = -12 + 26`

`=> A = 14`

A=[(26-2):4+1].(2-4)

A=[24:4+1].(-2)

A=7.(-2)

A=-14

B1:

\(a.301^2=\left(300+1\right)^2=300^2+2.300.1+1^2\\ =90000+600+1=90601\\ b.88^2+2.88.12+12^2=\left(88+12\right)^2=100^2=10000\\ c.99.100=100^2-100=10000-100=9900\\ d,153^2+94.153+47^2=153^2+2.153.47+47^2=\left(153+47\right)^2=200^2=40000\)

B2:

\(A=x^2-20x+101\\ =x^2-2.x.10+10^2+1\\ =\left(x-10\right)^2+1\ge1\forall x\in R\left(Vì:\left(x-10\right)^2\ge0\forall x\in R\right)\\ \Rightarrow min_A=1\Leftrightarrow x-10=0\Leftrightarrow x=10\)

Tính nhanh :

\(978^2+22^2+978.44\)

= \(978^2+2.978.22+22^2\)

= \(\left(978+22\right)^2=\left(1000\right)^2=1000000\)

tính :

\(x^2+6x+9\)

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

= \(\left(x+3\right)^2\)

Thay x = 997 vào BT ( x+ 3)² ta được :

\(\left(997+3\right)^2=\left(1000\right)^2=1000000\)

Vậy tại x = 997 GT của BT (x + 3)² là 1000000

\(x^2+6x+9=\left(x+3\right)^2=\left(997+3\right)^2=\left(1000^2\right)=1000000\)

a: \(68^2+64\cdot68+32^2\)

\(=\left(68+32\right)^2\)

=10000

b: \(51\cdot49=50^2-1=2499\)