Question

17. Desfaceți parantezele şi reduceți termenii asemenea: a) 3(2x³-5x² + 4x-7)-2(4x³-6x²-5x+3)-4(-x³ + 2x² + 3x-6); b) 2(3x³-7x² +6x-5)-3(5x³-3x² +7x-4)-4(-2x²-x²+3x+2); c) 4(4x²-5x²-3x-2)-3(3x³-4x²-5x-6)-2(2x³-3x² - 4x+5).​

Answer 1

Răspuns:

A) 2x3−11x2+10x−3

B) −9x3+7x2−21x−6

C) 13x3+14x2+11

PS:cand e un nr dupa x e la puterea de ex x2 e x la puterea a2a

Explicație pas cu pas:

a) 3(2x3−5x2+4x−7)−2(4x3−6x2−5x+3)−4(−x3+2x2+3x−6)

=(3)(2x3)+(3)(−5x2)+(3)(4x)+(3)(−7)+(−2)(4x3)+(−2)(−6x2)+(−2)(−5x)+(−2)(3)+(−4)(−x3)+(−4)(2x2)+(−4)(3x)+(−4)(−6)

=6x3+−15x2+12x+−21+−8x3+12x2+10x+−6+4x3+−8x2+−12x+24

=(6x3+−8x3+4x3)+(−15x2+12x2+−8x2)+(12x+10x+−12x)+(−21+−6+24)

=2x3+−11x2+10x+−3

b) 2(3x3−7x2+6x−5)−3(5x3−3x2+7x−4)−4(−2x2−x2+3x+2)

=(2)(3x3)+(2)(−7x2)+(2)(6x)+(2)(−5)+(−3)(5x3)+(−3)(−3x2)+(−3)(7x)+(−3)(−4)+(−4)(−2x2)+(−4)(−x2)+(−4)(3x)+(−4)(2)

=6x3+−14x2+12x+−10+−15x3+9x2+−21x+12+8x2+4x2+−12x+−8

=(6x3+−15x3)+(−14x2+9x2+8x2+4x2)+(12x+−21x+−12x)+(−10+12+−8)

=−9x3+7x2+−21x+−6

C) 4(4x2−5x2−3x−2)−3(3x3−4x2−5x−6)−2(2x3−3x2−4x+5)

=(4)(4x2)+(4)(−5x2)+(4)(−3x)+(4)(−2)+(−3)(3x3)+(−3)(−4x2)+(−3)(−5x)+(−3)(−6)+(−2)(2x3)+(−2)(−3x2)+(−2)(−4x)+(−2)(5)

=16x2+−20x2+−12x+−8+−9x3+12x2+15x+18+−4x3+6x2+8x+−10

=(−9x3+−4x3)+(16x2+−20x2+12x2+6x2)+(−12x+15x+8x)+(−8+18+−10)

=−13x3+14x2+11

Answer 2

Răspuns:

Explicație pas cu pas:

17. Desfaceți parantezele şi reduceți termenii asemenea:

a) 3(2x³-5x² + 4x-7)-2(4x³-6x²-5x+3)-4(-x³ + 2x² + 3x-6)=

6x³-15x²+12x-21-8x³+12x²+10x-6+4x³-8x²-12x+24= 6x³-8x³+4x³-15x²+12x²-8x²+12x+10x-12x-21-6+24= 2x³-11x²+10x-3

b) 2(3x³-7x² +6x-5)-3(5x³-3x² +7x-4)-4(-2x²-x²+3x+2)=

2(3x³-7x² +6x-5)-3(5x³-3x² +7x-4)-4(-3x²+3x+2)=

6x³-14x²+12x-10-15x³+9x²-21x+12+12x²-12x-8=

6x³-15x³-14x²+9x²+12x²+12x-21x-12x-10+12-8=-9x³+7x²-21x-6

Rezolvarea alternativa de mai jos este pentru -4(-2x³-x²+3x+2) la ultima paranteza, adica am presupus ca a fost scris gresit x² in loc de x³.

2(3x³-7x² +6x-5)-3(5x³-3x² +7x-4)-4(-2x³-x²+3x+2)=

6x³-14x²+12x-10-15x³+9x²-21x+12+8x³+4x²-12x-8=

6x³-15x³+8x³-14x²+9x²+4x²+12x-21x-12x-10+12-8=-x³-x²-21x-6

c) 4(4x²-5x²-3x-2)-3(3x³-4x²-5x-6)-2(2x³-3x²-4x+5)=

4(-x²-3x-2)-3(3x³-4x²-5x-6)-2(2x³-3x²-4x+5)=

-4x²-12x-8-9x³+12x²+15x+18-4x³+6x²+8x-10=

-9x³-4x³-4x²+12x²+6x²-12x+15x+8x-8+18-10=-13x³+14x²+11x

Rezolvarea alternativa de mai jos este pentru 4(4x²-5x²-3x-2) la prima paranteza, adica am presupus ca a fost scris gresit x² in loc de x³.

4(4x³-5x²-3x-2)-3(3x³-4x²-5x-6)-2(2x³-3x² - 4x+5)=

16x³-20x²-12x-8-9x³+12x²+15x+18-4x³+6x²+8x-10=

16x³-9x³-4x³-20x²+12x²+6x²-12x+15x+8x-8+18-10=3x³-2x²+11x