Question

1) Піднести до квадрата двочлен: а) (2m-5)² б) (3a²-b³)²2) Подати у вигляді степення: а) x²-14+493) Спростити:а) b•(b-3)-(b-4)²​

Answer 1

Відповідь: прикріпив відповідь

Answer 2

1) Піднести до квадрата двочлен:

а) (2m-5)²

To square the binomial (2m-5), we can use the formula (a - b)² = a² - 2ab + b². In this case, a = 2m and b = 5.

So, let's substitute the values into the formula:

(2m-5)² = (2m)² - 2(2m)(5) + (5)²

Expanding the expression:

= 4m² - 20m + 25

Therefore, (2m-5)² simplifies to 4m² - 20m + 25.

б) (3a²-b³)²

To square the binomial (3a²-b³), we can again use the formula (a - b)² = a² - 2ab + b². In this case, a = 3a² and b = b³.

Substituting the values into the formula:

(3a²-b³)² = (3a²)² - 2(3a²)(b³) + (b³)²

Expanding the expression:

= 9a^4 - 6a²b³ + b⁶

Therefore, (3a²-b³)² simplifies to 9a^4 - 6a²b³ + b⁶.

2) Подати у вигляді степення:

а) x² - 14x + 49

To express the quadratic expression x² - 14x + 49 as a perfect square, we need to complete the square.

First, let's take half of the coefficient of x (-14) and square it:

(-14/2)² = (-7)² = 49

Now, we can add and subtract 49 within the expression:

x² - 14x + 49 = x² - 14x + 49 - 49 + 49

Simplifying:

= (x - 7)²

Therefore, x² - 14x + 49 can be expressed as (x - 7)².

3) Спростити:

а) b • (b - 3) - (b - 4)²

To simplify the expression b • (b - 3) - (b - 4)², let's expand the squared term first.

(b - 4)² = (b - 4)(b - 4)

Using the FOIL method to expand the expression:

= b² - 4b - 4b + 16

= b² - 8b + 16

Now, let's substitute this expression back into the original equation:

b • (b - 3) - (b - 4)² = b • (b - 3) - (b² - 8b + 16)

Expanding the first term:

= b² - 3b - b² + 8b - 16

Combining like terms:

= -3b + 8b - 16

= 5b - 16

Therefore, b • (b - 3) - (b - 4)² simplifies to 5b - 16.