Question

24. Descompuneti in produs de factori:
d.(8x-3)²-(2x+5)²
e.(4x+1)²-(x²-4x)²
f. (4x²-(x²-5x)²

37. Descompuneti in produs de factori:
g. x⁵-16x
h. 64x⁷-x​

Answer 1

Răspuns:

Explicație pas cu pas:

d) (8x-3)²-(2x+5)² = a²-b² = (a-b)(a+b) = (8x-3-2x-5)(8x-3+2x+5) =

= (6x-8)(10x+2) = 4·(3x-4)(5x+1)

e) (4x+1)²-(x²-4x)² = (4x+1-x²+4x)(4x+1+x²-4x) =

= (-x²+8x+1)(x²+1)

f) (4x)²-(x²-5x)² = (4x-x²+5x)(4x+x²-5x) = (-x²+9x)(x²-x) =

= x²·(9-x)(x-1)

f') (4x²) - (x²-5x)² = (2x-x²+5x)(2x+x²-5x) = (-x²+7x)(x²-3x) =

= x²·(7-x)(x-3)

g)  x⁵-16x = x(x⁴-16) = x(x²-4)(x²+4) = x(x-2)(x+2)(x²+4)

h) 64x⁷-x​ = x(64x⁶-1) = x(8x³-1)(8x³+1) =

= x(2x-1)(4x²+2x+1)(2x+1)(4x²-2x+1)