Question

Выполните действия, используя формулы сокращённого умножения ​

Answer 1

373

1.

${(90 - 1)}^{2} = {90}^{2} - 180 + 1 = \\ = 8100 - 179 = 7921$

2.

${(40 + 1)}^{2} = {40}^{2} + 80 + 1 = \\ = 1600 + 81 = 1681$

3.

${101}^{2} = {(100 + 1)}^{2} = \\ = {100}^{2} + 200 + 1 = \\ = 10000 + 201 = 10201$

4.

${98}^{2} = {(100 - 2)}^{2} = \\ = {100}^{2} - 400 + 4 = \\ = 10000 - 396 = 9604$

374

1.

${999}^{2} = {(1000 - 1)}^{2} = \\ = {1000}^{2} - 2000 + 1 = \\ = 1000000 - 1999 = 998001$

2.

${1003}^{2} = {(1000 + 3)}^{2} = \\ = {1000}^{2} + 6000 + 9 = \\ = 1000000 + 6009 = 1006009$

3.

${51}^{2} = {(50 + 1)}^{2} = \\ = {50}^{2} + 100 + 1 = \\ = 2500 + 101 = 2601$

4.

${39}^{2} = {(40 - 1)}^{2} = \\ = {40}^{2} - 80 + 1 = \\ = 1600 - 79 = 1521$

375

1.

${72}^{2} = {(70 + 2)}^{2} = \\ = {70}^{2} + 280 + 4 = \\ = 4900 + 284 = 5184$

2.

${57}^{2} = {(60 - 3)}^{2} = \\ = 3600 - 360 + 9 = \\ 3600 - 351 = 3249$

3.

${997}^{2} = {(1000 - 3)}^{2} = \\ = 1000000 - 6000 + 9 = \\ = 994009$

4.

${1001}^{2} = {(1000 + 1)}^{2} = \\ = 1000000 + 2000 + 1 = \\ = 1002001$