Question

Exersare

2. Restrange Patratul unei sume sau al unei diferente :
a)x²-12x+36; b) 25x²+10x+1; ; c) 25+40x+16x²; d) 9x²-12x+4

3. Descompune folosind formula diferentei de patrate
a) x²-64; b) 9x²-4; c) 25x²-16 ; d) 4x²-25

4. Descompune
a) 8x+8y-ax-ay;
b) x³+x²+4x+4;
c) x³+x²-25(x+1);

Answer 1

Răspuns:

$2)a) {x}^{2} - 12x + 36 = (x - 6) ^{2} \\ b)25 {x}^{2} + 10x + 1 = ( {5x + 1)}^{2} \\ c)25 + 40x + 16 {x}^{2} = {(4x + 5)}^{2} \\ d)9 {x}^{2} - 12x + 4 = ( {3x - 2)}^{2}$

$3)a) {x}^{2} - 64 = {x}^{2} - {8}^{2} = (x - 8)(x + 8) \\ b)9 {x}^{2} - 4 =( 3 {x)}^{2} - {2}^{2} = (3x - 2)(3x + 2) \\ c)25 {x}^{2} - 16 = (5 {x})^{2} - {4}^{2} = (5x - 4)(5x + 4) \\ d)4 {x}^{2} - 25 =( 2 {x})^{2} - {5}^{2} = (2x - 5)(2x + 5)$

$4)a)8x + 8y - ax - ay = 8(x + y) - a(x + y) = (x + y)(8 - a)$

$b) {x}^{3} + {x}^{2} + 4x + 4 = x( {x}^{2} + x + 4) + 4$

$c) {x}^{3} + {x}^{2} - 25(x + 1) = {x}^{2} (x + 1) - 25(x + 1) = (x + 1)( {x}^{2} - 25)$

Answer 2

2. a) (x-6)^2
b) (5x+1)^2
C) (5+4x)^2
D) (3x-2)*2
Ex. Se rezolva pe baza formulei, dacă o știi nu ar trebui sa ai vreo problema