Question

Calculati : 1) ( 3x + 5 ) la puterea 2 + ( 5x -3 ) la puterea 2
2) ( 3 - 2a ) la puterea 2 - ( 4a + 1 ) la puterea 2 + ( 4a -5 ) (4a + 5 ) .
Aratati-mi va rog si rezolvarea . Multumesc.

Answer 1

1)
(3x+5)² + (5x-3)² 

(3x+5)² = (3x)² + 2·3x·5 + 5² = 9x² + 30x + 25
(5x-3)² = (5x)² - 2·5x·3 + 3² = 25x² - 30x + 9

9x² + 30x + 25 + 25x² - 30x + 9 =
= 34x² + 34 =
= 34(x² + 1)

2) (3-2a)² - (4a+1)² + (4a-5)(4a+5) 

(3-2a)² = 3² - 2·3·2a + (2a)² = 9 - 12a + 4a² = 4a² - 12a + 9
(4a+1)² = (4a)² + 2·4a·1 + 1² = 16a² + 8a + 1
(4a-5)(4a+5) = (4a)² - 5² = 16a² - 25

4a² - 12a + 9 - (16a² + 8a + 1) + 16a² - 25 =
= 4a² - 12a + 9 - 16a² - 8a - 1 + 16a² - 25 =
= 4a² - 20a - 16 

Sper ca te-am ajutat :)

Answer 2

(3-2a)²-(4a+1)²+(4a-5)(4a+5)=

(3-2a)²=3²-2×3×2a+4a²=9-12a+4a²=4a²-12a+9;
(4a+1)²=(4a)²+2×4a×1+1²=16a²+8a+1;

(4a-5)(4a+5)=(4a)²-5²=16a²-25;
4a²-12a+9-16a²-8a-1+16a²-25=4a²-20a-17