Question

9.31 a) (y + 2)² – 4y?,6) 100a²– (5a + а)²;B) (t - 7) - 9t²;r) 121b²- (7b- 3)².​

Answer 1

Ответ:

У нас есть формулы сокращённого умножения: (а+b) ²=а ²+2ab+b ²;

(а-b) ²=а ²-2ab+b ²

Применим их:

а) (y + 2)² – 4y=у ²+4у+4-4у=у ²+4

б) 100a²– (5a + а)²=100а ²-(6а) ²=100a ²-36a ²=64a ²

в) (t - 7) - 9t²= t-7-9t ².

г) 121b²- (7b- 3)²=121b ²-(49b ²-42b+9)=

121b ²-49b ²+42b-9=72b ²+42b-9

Answer 2

Let's simplify the given expressions:

a) (y + 2)² - 4y:

First, expand the square:

(y + 2)² = y² + 4y + 4

Now, subtract 4y:

(y + 2)² - 4y = (y² + 4y + 4) - 4y = y² + 4

So, the simplified expression is y² + 4.

b) 100a² - (5a + а)²:

First, expand the square:

(5a + a)² = (6a)² = 36a²

Now, subtract it from 100a²:

100a² - 36a² = 64a²

So, the simplified expression is 64a².

r) 121b² - (7b - 3)²:

First, expand the square:

(7b - 3)² = (7b)² - 2(7b)(3) + 3² = 49b² - 42b + 9

Now, subtract it from 121b²:

121b² - (49b² - 42b + 9) = 121b² - 49b² + 42b - 9

Now, combine like terms:

121b² - 49b² + 42b - 9 = 72b² + 42b - 9

So, the simplified expression is 72b² + 42b - 9.

I noticed that in the expression for part b, there is a Cyrillic 'а' and a Latin 'a.' If they should be the same variable, you can simplify it as follows:

100a² - (5a + a)² = 100a² - (6a)² = 100a² - 36a² = 64a²