Question

8Folosind formulele de calcul prescurtat potrivite, calculați: a) (7a + 5)^2; (3b – 5c)^2; (2u + v)(2u – v); b) (1/2 a + 3)^2; (2/3 x – 3y)^2; (1/3 a + 1/2 b)(1/a – 1/2) b ; c) ( √5 a + 3)^2; ( √2 − √3y )^2; ( √2p + √5q)( √2p – √5q). Dau coroana

Answer 1

Răspuns:

8 Folosind formulele de calcul prescurtat potrivite, calculați:

a)

(7a + 5)^2 = (7a)^2 + 2 x 7a x 5 + 5^2 =  49a^2 + 70a + 25;

(3b – 5c)^2 = (3b)^2 - 2 x 3b x 5c - (5c)^2 =  9b^2 - 30bc + 25c^2;

(2u + v)(2u – v) = (2u)^2 - v^2 =  4u^2 - v^2;

b)

(1/2 a + 3)^2 = (1/2 a)^2 + 2 x 1/2 a x 3 + 3^2 = 1/4 a^2 + 3a + 9;

(2/3 x – 3y)^2 = (2/3 x)^2 - 2 x 2/3 X x 3y + (3y)^2 =  3/9 x^2 - 4xy + 9y^2;

(1/3 a + 1/2 b)(1/3 a – 1/2 b) = (1/3 a)^2 - (1/2 b)^2 = 1/9 a^2  -  1/4 b^2;

c)

( √5 a + 3)^2 = (√5 a)^2 + 2 x √5 a x 3 + 3^2 = 5a^2 + 6a√5 + 9;

( √2 − √3y )^2 = (√2)^2 - 2 x √2 x √3 y + (√3 y)^2 =  2 - 2y√6 + 3y^2;

( √2p + √5q)( √2p – √5q) =  (√2 p)^2 - (√5 g)^2 = 2p^2 - 5g^2

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