a) −4x2(x−7)+4x(x2−5)−28x2-4x^2(x - 7) + 4x(x^2 - 5) - 28x^2−4x2(x−7)+4x(x2−5)−28x2
−4x2(x−7)+4x(x2−5)−28x2=−4x3+28x2+4x3−20x−28x2-4x^2(x - 7) + 4x(x^2 - 5) - 28x^2 = -4x^3 + 28x^2 + 4x^3 - 20x - 28x^2−4x2(x−7)+4x(x2−5)−28x2=−4x3+28x2+4x3−20x−28x2 =(−4x3+4x3)+(28x2−28x2)−20x= (-4x^3 + 4x^3) + (28x^2 - 28x^2) - 20x=(−4x3+4x3)+(28x2−28x2)−20x =−20x= -20x=−20x
b) x(1−x)+(x+1)2x(1 - x) + (x + 1)^2x(1−x)+(x+1)2
x(1−x)+(x+1)2=x−x2+(x2+2x+1)x(1 - x) + (x + 1)^2 = x - x^2 + (x^2 + 2x + 1)x(1−x)+(x+1)2=x−x2+(x2+2x+1) =(−x2+x2)+(x+2x)+1= (-x^2 + x^2) + (x + 2x) + 1=(−x2+x2)+(x+2x)+1 =3x+1= 3x + 1=3x+1
c) (x−3)(x+3)−(x−5)2(x - 3)(x + 3) - (x - 5)^2(x−3)(x+3)−(x−5)2
(x−3)(x+3)=x2−9(x - 3)(x + 3) = x^2 - 9(x−3)(x+3)=x2−9 (x−5)2=x2−10x+25(x - 5)^2 = x^2 - 10x + 25(x−5)2=x2−10x+25 (x−3)(x+3)−(x−5)2=x2−9−(x2−10x+25)(x - 3)(x + 3) - (x - 5)^2 = x^2 - 9 - (x^2 - 10x + 25)(x−3)(x+3)−(x−5)2=x2−9−(x2−10x+25) =x2−9−x2+10x−25= x^2 - 9 - x^2 + 10x - 25=x2−9−x2+10x−25 =10x−34= 10x - 34=10x−34
d) (x+1)3−(x−4)(x+4)−x3(x + 1)^3 - (x - 4)(x + 4) - x^3(x+1)3−(x−4)(x+4)−x3
(x+1)3=x3+3x2+3x+1(x + 1)^3 = x^3 + 3x^2 + 3x + 1(x+1)3=x3+3x2+3x+1 (x−4)(x+4)=x2−16(x - 4)(x + 4) = x^2 - 16(x−4)(x+4)=x2−16 (x+1)3−(x−4)(x+4)−x3=(x3+3x2+3x+1)−(x2−16)−x3(x + 1)^3 - (x - 4)(x + 4) - x^3 = (x^3 + 3x^2 + 3x + 1) - (x^2 - 16) - x^3(x+1)3−(x−4)(x+4)−x3=(x3+3x2+3x+1)−(x2−16)−x3 =(x3−x3)+3x2−x2+3x+1+16= (x^3 - x^3) + 3x^2 - x^2 + 3x + 1 + 16=(x3−x3)+3x2−x2+3x+1+16 =2x2+3x+17= 2x^2 + 3x + 17=2x2+3x+17
e) 2(3x−1)(2x+5)−6(2x−1)(x+2)2(3x - 1)(2x + 5) - 6(2x - 1)(x + 2)2(3x−1)(2x+5)−6(2x−1)(x+2)
2(3x−1)(2x+5)=2(6x2+13x−5)=12x2+26x−102(3x - 1)(2x + 5) = 2(6x^2 + 13x - 5) = 12x^2 + 26x - 102(3x−1)(2x+5)=2(6x2+13x−5)=12x2+26x−10 6(2x−1)(x+2)=6(2x2+3x−2)=12x2+18x−126(2x - 1)(x + 2) = 6(2x^2 + 3x - 2) = 12x^2 + 18x - 126(2x−1)(x+2)=6(2x2+3x−2)=12x2+18x−12 2(3x−1)(2x+5)−6(2x−1)(x+2)=(12x2+26x−10)−(12x2+18x−12)2(3x - 1)(2x + 5) - 6(2x - 1)(x + 2) = (12x^2 + 26x - 10) - (12x^2 + 18x - 12)2(3x−1)(2x+5)−6(2x−1)(x+2)=(12x2+26x−10)−(12x2+18x−12) =12x2−12x2+26x−18x−10+12= 12x^2 - 12x^2 + 26x - 18x - 10 + 12=12x2−12x2+26x−18x−10+12 =8x+2= 8x + 2=8x+2