Question

1. Өрнекті ықшамдаңдар: а) (4a + 7) ^ 2 ;б)(6x-5y)^ 2 ; в) (y ^ 2 - x ^ 3) ^ 2​

Answer 1

Ответ:

а) 16а² + 56а + 49 ;

б) 36х² - 60ху + 25у²;

в) у^4 - 2х³у² + х^6.

Объяснение:

а) (4a + 7)² = (4а)² + 2•4а•7 + 7² = 16а² + 56а + 49 ;

б)(6x-5y)² = (6х)² - 2•6х•5у + (5у)² = 36х² - 60ху + 25у² ;

в) (y² - x³) ² = (у²)² - 2•у²•х³ - (х³)² = у^4 - 2х³у² + х^6.

Answer 2

1. (4a + 7) ^ 2:

(4a + 7) ^ 2 = (4a + 7) * (4a + 7)

To expand this expression, you can use the FOIL (First, Outer, Inner, Last) method:

First: (4a * 4a) = 16a^2 Outer: (4a * 7) = 28a Inner: (7 * 4a) = 28a Last: (7 * 7) = 49

Now, combine these terms:

16a^2 + 28a + 28a + 49

Combine like terms:

16a^2 + 56a + 49

So, (4a + 7) ^ 2 = 16a^2 + 56a + 49.

2. (6x - 5y) ^ 2:

(6x - 5y) ^ 2 = (6x - 5y) * (6x - 5y)

Again, use the FOIL method:

First: (6x * 6x) = 36x^2 Outer: (6x * -5y) = -30xy Inner: (-5y * 6x) = -30xy Last: (-5y * -5y) = 25y^2

Combine these terms:

36x^2 - 30xy - 30xy + 25y^2

Combine like terms:

36x^2 - 60xy + 25y^2

So, (6x - 5y) ^ 2 = 36x^2 - 60xy + 25y^2.

3. (y^2 - x^3) ^ 2:

(y^2 - x^3) ^ 2 = (y^2 - x^3) * (y^2 - x^3)

Using FOIL:

First: (y^2 * y^2) = y^4 Outer: (y^2 * -x^3) = -x^3y^2 Inner: (-x^3 * y^2) = -x^3y^2 Last: (-x^3 * -x^3) = x^6

Combine these terms:

y^4 - x^3y^2 - x^3y^2 + x^6

Combine like terms:

y^4 - 2x^3y^2 + x^6

So, (y^2 - x^3) ^ 2 = y^4 - 2x^3y^2 + x^6.