Question

Descompuneți, folosind formula diferenţei de pătrate:
b)x²-64;
e) 9x²-4;
h) x²-100;
b) (x + 5)²-9;
e) (x-3)²-25;
h) (4x - 1)² - 4x²;
A. a) x²-16;
d) x²-36;
g) 4x²-25;
B. a) (2x + 1)2-4;
d) (3x + 2)²-100;
g) (2x+3)²-x²;
Oplicare si exersare
**
c) x²-25;
f) 25x²-16;
i) 9x² - 64.
c) (x + 4)² - 1;
f) (x-7)²-64;
i) (3x-4)²-9x².

Answer 1

Răspuns:

Explicație pas cu pas:

a) x²-16 = x²-4² = (x-4)(x+4)

b) x²-64 = x²-8² = (x-8)(x+8)

c) x²-25 = x²-5² = (x-5)(x+5)

d) x²-36 = x²-6² = (x-6)(x+6)

e) 9x²-4 = (3x)²-2² = (3x-2)(3x+2)

f) 25x²-16 = (5x)²-4² = (5x-4)(5x+4)

g) 4x²-25 = (2x)²-5² = (2x-5)(2x+5)

h) x²-100 = x²-10² = (x-10)(x+10)

i) 9x² - 64 = (3x)²-8² = (3x-8)(3x+8)

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a) (2x + 1)²-4 = (2x+1-2)(2x+1+2) = (2x-1)(2x+3)

b) (x + 5)²-9 = (x+5-3)(x+5+3) = (x+2)(x+8)

c) (x + 4)² - 1 = (x+4-1)(x+4+1) = (x+3)(x+5)

d) (3x + 2)²-100 = (3x+2-10)(3x+2+10) = (3x-8)(3x+12)

e) (x-3)²-25 = (x-3-5)(x-3+5) = (x-8)(x+2)

f) (x-7)²-64 = (x-7-8)(x-7+8) = (x-15)(x+1)

g) (2x+3)²-x² = (2x+3-x)(2x+3+x) = (x+3)(3x+3) = 3(x+3)(x+1)

h) (4x - 1)² - 4x² = (4x-1-2x)(4x-1+2x) = (2x-1)(6x-1)

i)  (3x-4)²-9x² = (3x-4-3x)(3x-4+3x) = -4(6x-4) = -8(3x-2)