Question

EX 4 TE ROG SLAVITESCUDORAA TE ROGGGG​

Answer 1

a) (a²-1)(a²+1)=(a-1)(a+1)(a²+1)

(a²-4)(a²+4)=(a-2)(a+2)(a²+4)

(x²-a²)(x²+a²)=(x-a)(x+a)(x²+a²)

b) (a²-7²)(a²+7²)=(a²-49)(a²+49)=(a-7)(a+7)(a²+49)

(b²-4c²)(b²+4c²)=(b-2c)(b+2c)(b²+4c²)

0,0001=1/10000

1/10000-x^4=1/10000(1-10000x^4)=1/10000(1-100x²)(1+100x²)=1/10000(1-10x)(1+10x)(1+100x²)

c) 1/625(1-625x^4)=1/625(1-25x²)(1+25x²)=1/625(1-5x)(1+5x)(1+25x²)

1/81(81a^4-1)=1/81(9a²-1)(9a²+1)=1/81(3a-1)(3a+1)(9a²+1)

1/16(81-16x^4)=1/16(9-4x²)(9+4x²)=1/16(3-2x)(3+2x)(9+4x²)

d) 2²-x²*x²=2²-(x²)²=(2-x²)(2+x²)

[(x²-1)(x²+1)]-(x+1)^4=[(x-1)(x+1)(x²+1)]-(x+1)^4=(x-1)(x+1)(x²+1)-(x+1)^4=(x+1)[(x-1)(x²+1)-(x+1)³]=(x+1)[x^3+x-x²-1-(x³+3x²+3x+1)]=(x+1)(x³+x-x²-1-x³-3x²-3x-1)=(x+1)[2(x+2x²+1)]

e) x^4+x²+1+2x³+2x²+2x-x²+x-1= x^4+2x³+2x²+3x

f) 16x^4+x²+1+8x³+8x²+2x-4x²+x-1= 16x^4+5x²+8x³+3x

g) 4x^4+x²+1+4x³+4x²+2x-2x²+x-1= 4x^4+3x²+4x³+3x

h) 9x^4+4x²+1-12x³+6x²-4x-3x²-2x-1= 9x^4+7x²-12x³-6x

i) x^4+49x²+1-14x³-2x²+14x-x²+7x-1= x^4+46x²-14x³+21x