a)  mk chỉnh đề

 \(978^2+22^2+978.44=\left(978+22\right)^2=100^2=10000\)

b)   \(52.48=\left(50+2\right)\left(50-2\right)=50^2-2^2=2496\)

c) mk chỉnh đề

  \(821^2+321^2-821.642=\left(821-321\right)^2=500^2=250000\)

a) \(978^2+22^2+978.44=978^2+2.22.978+22^2=\left(978+22\right)^2=1000^2=1000000\)

b) \(52.48=\left(50+2\right).\left(50-2\right)=50^2-2^2=2500-4=2496\)

c) Có nhầm dấu không bạn ơi. Mình sửa luôn nha

821² + 321² - 821.642 = 821² - 2.821.321 + 321² = (821-321)² = 500² = 250 000

a)   \(978^2+22^2+978.22\)

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

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

b)   \(821^2+321^2-821.642\)

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

a. A = (a + b)³ - (a - b)³

A = \(\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

A = (a + b - a + b)\(\left[a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right]\)

A = 2b(a² + a² + a² + 2ab - 2ab + b² - b² + b²)

A = 2b(3a² + b²)

A = 6a²b + 2b³

Tách ra mỗi câu một lần.

Dài quá không ai làm đâu.

Nhìn nản lắm.

Câu 3: 

a: \(49^2=2401\)

b: \(51^2=2601\)

c: \(99\cdot100=9900\)

Bài 2.

a) 101³ = (100+1)³ = 100³+3.100².1+3.100.1²+1³ 

   = 1000000+30000+300+1 = 1030301

b) 299³ = (300-1)³ = 300³-3.300².1+3.300.1²-1³

   = 27000000 - 270000 + 900 -1 = 26730899

c) 99³ = (100-1)³ = 100³-3.100².1+3.100.1²-1

   = 1000000 - 30000 + 300 -1 = 970299

\(1,\\ b,A=\left(u-v\right)^3+3uv\left(u+v\right)\\ A=u^3-3u^2v+3uv^2-v^3+3u^2v+3uv^2=u^3-v^3\\ c,6\left(c-d\right)\left(c+d\right)+2\left(c-d\right)^2-\left(c-d\right)^3\\ =6c^2-6d^2+2c^2-4cd+2d^2-c^3+3c^2d-3cd^2+d^3\\ =8c^2-c^3-4d^2-4cd+3c^2d-3cd^2+d^3\)

\(2,\\ a,101^3=\left(100+1\right)^3\\ =100^3+3\cdot10000\cdot1+3\cdot100\cdot1+1\\ =1000000+30000+300+1=1030301\\ b,299^3=\left(300-1\right)^3\\ =300^3-3\cdot90000\cdot1+3\cdot300\cdot1-1\\ =27000000-270000+900-1\\ =26730899\\ c,99^3=\left(100-1\right)^3\\ =100^3-3\cdot10000\cdot1+3\cdot100\cdot1-1\\ =1000000-30000+300-1=970299\)

a) \(82\cdot78\)

\(=\left(80+2\right)\cdot\left(80-2\right)\)

\(=80^2-2^2\)

\(=6400-4\)

\(=6396\)

b) \(87\cdot93\)

\(=\left(90-3\right)\left(90+3\right)\)

\(=90^2-3^2\)

\(=8100-9\)

\(=8091\)

c) \(125^2-25^2\)

\(=\left(125-25\right)\left(125+25\right)\)

\(=100\cdot150\)

\(=15000\)

`a, 38 . 42 = (40-2)(40+2) = 1600 - 4 = 1596`.`

`b, 102^2 = (100+2)^2 = 10000 + 400 + 4 = 10404`

`c, 198^2 = (200-2)^2 = 40000 - 800 + 4 = 39204`

`d, 75^2 - 25^2 = (75+25)(75-25) = 100. 50 = 5000`

a) \(41\cdot24-41\cdot14+59\cdot24-59\cdot14\)

\(=41\cdot10+59\cdot10\)

\(=1000\)