Question

А) (р+1)2-(р+2)2 ; б) 2(2ав-в2)+2(а-в)2 ; в) (7-х)(7+х)+(х+3)2

Answer 1

Ответ:

a)(p+1)²-(p+2)²=р²+2р+1-р²-2р-4= -3

Б)2(2ab-b²)+2(a-b)²=4ab-2b²+2(a²-2ab+b²)= 4ab-2b²+2a²-2ab+2b²=2ab+2a²

в)(7-х)(7+х)+(х+3)²=49-х²+х²+6х+9=40+6х

Answer 2

Let's simplify each expression:

А) (р+1)2 - (р+2)2

To simplify, let's expand the squares:

(р + 1)2 = (р + 1)(р + 1) = р2 + 2р + 1 (р + 2)2 = (р + 2)(р + 2) = р2 + 4р + 4

Now, subtract the second expression from the first:

(р + 1)2 - (р + 2)2 = (р2 + 2р + 1) - (р2 + 4р + 4)

Remove the parentheses and simplify further:

= р2 + 2р + 1 - р2 - 4р - 4

Combine like terms:

= (р2 - р2) + (2р - 4р) + (1 - 4)

= 0 - 2р - 3

So, the simplified expression is: -2р - 3.

Б) 2(2ав - в2) + 2(а - в)2

First, let's expand the squared term:

(а - в)2 = (а - в)(а - в) = а2 - 2ав + в2

Now, substitute the squared term back into the expression:

2(2ав - в2) + 2(а - в)2 = 2(2ав - в2) + 2(а2 - 2ав + в2)

Now, distribute the 2 to each term:

= 4ав - 2в2 + 2а2 - 4ав + 2в2

Combine like terms:

= 4ав - 4ав + 2а2

Now, you can factor out a common term:

= 2а(2в - 2а)

Finally, you can simplify further by factoring out a 2 from the parentheses:

= 2а(2(в - а))

So, the simplified expression is: 2а(2(в - а)).

В) (7 - х)(7 + х) + (х + 3)2

Let's first expand the squared term:

(х + 3)2 = (х + 3)(х + 3) = х2 + 6х + 9

Now, substitute the squared term back into the expression:

(7 - х)(7 + х) + (х + 3)2 = (7 - х)(7 + х) + (х2 + 6х + 9)

Now, let's use the difference of squares formula: (a - b)(a + b) = a2 - b2

= 7^2 - х^2 + х2 + 6х + 9

The х^2 and -х^2 terms cancel each other out:

= 49 + 6х + 9

Combine the constants:

= 58 + 6х

So, the simplified expression is: 58 + 6х.