Question

Tema matematica please ajutatima :

1. Descompuneti in factori primi , folosind formulele de calcul prescurtat:
a. $121x^{2} - 144 y^{2}$
b. $( a+1)^{2} -4$
c. $9-( 2b+3)^{2}$
d. $16c^{2} -( 3c+5d)^{2}$
e. $9( 5m-4p)^{2} - 64m^{2}$
f . $( n+3q)^{2} - 4 (q-n)^{2}$
g. $a^{2} + 6a +9$
h. $-30ab^{2} + 25b^{4} + 9a^{2}$

2. Descompuneti in factori :
a. $36x^{3} - x$
b. $20x^{2} - 5y^{2}$
c. $9 xy^{2} - 9$
d. $x^{2} +2xy +y- z^{2}$

Answer 1

1. a) 121x² - 144y² = (11x + 12y)(11x - 12y)
b) (a + 1)² - 4 = a² + 2a + 1 - 4 = a² + 2a - 3
c) 9 - (2b + 3)² = 9 - (4b² + 12b + 9) = 9 - 4b² - 12b - 9 = - 4b(b + 3)
d) 16c² - (3c + 5d)² = 16c² - (9c² + 30cd + 25d²) = 7c² - 30cd - 25d²
e) 9(5m - 4p)² - 64m² = 9(25m² - 40mp + 16p²) - 64m² = 225m² - 360mp + 144p² - 64m² = 161m² - 360mp + 144p²
f) (n + 3q)² - 4(q - n)² = n² + 6nq + 9q² - 4(q²- 2nq + n²) = n² + 6nq + 9q² - 4q² + 8nq - 4n² = - 3n² + 14nq + 5q²
g) a² + 6a + 9 = (a + 3)² am restrans deoarece era deja descompus
h) - 30ab² + 25b^4 + 9a² = (3a - 5b²)²
2.
a) 36x³ - x = x(36x² - 1) = x(6x + 1)(6x - 1)
b) 20x² - 5y² = 5 (4x² -y²) = 5(2x + y)(2x - y)
c) 9xy² - 9 = 9(xy² - 1)
d) x² + 2xy + y - z² = (x + y)² - z² = (x + y + z)(x + y - z)