Question

Answer 1

Bài 2.

a. $(x-2)^2+(x-3)(x+3)-2x(x-5)$

$=(x^2-4x+4)+(x^2-9)-(2x^2-10x)$

$=x^2-4x+4+x^2-9-2x^2+10x$

$=6x-5$

b. 

$(x+1)^2+(x-5)(x+5)$

$=(x^2+2x+1)+(x^2-25)$

$=2x^2+2x-24$

c.

$(x-3)(x+3)+(x-5)(x+1)+(x-4)^2$

$=(x^2-9)+(x^2-4x-5)+(x^2-8x+16)$

$=x^2-9+x^2-4x-5+x^2-8x+16$

$=3x^2-12x+2$

d.

$(2x-1)^2-(x-1)(x+1)-3x(x+5)$

$=(4x^2-4x+1)-(x^2-1)-(3x^2+15x)$

$=4x^2-4x+1-x^2+1-3x^2-15x$

$=2-19x$

 

 

Answer 2

Bài 3.

a. $101^2=101^2-1^2+1=(101-1)(101+1)+1$

$=100.102+1=10200+1=10201$

b. $98^2=98^2-2^2+4=(98-2)(98+2)+4=96.100+4=9600+4$

$=9604$

d.

$73^2-27^2=(73-27)(73+27)=46.100=4600$

e.

$32^2+68^2+64.68=32^2+68^2+2.32.68$

$=(32+68)^2=100^2=10000$

h.

$47^2+53^2+106.47=47^2+53^2+2.53.47$

$=(47+53)^2=100^2=10000$

 

Answer 3

a) (x-2)²+(x-3)(x+3)-2x(x-5)

= x²-4x+4+x²-9-2x²+10x

= 6x-5

b) (x+1)²+(x-5)(x+5)

= x²+2x+1+x²-25

=2x²+2x-24

c) (x-3)(x+3)+(x-5)(x+1)+(x-4)²

=x²-9+x²-5x+x-5+x²-8x+16

=3x²-12x+2

d) (2x-1)²-(x-1)(x+1)-3x(x+5)

=4x²-4x+1-x²-1-3x²-15x

=-19x

Answer 4

a) Ta có: \(\left(x-2\right)^2+\left(x-3\right)\left(x+3\right)-2x\left(x-5\right)\)

\(=x^2-4x+4+x^2-9-2x^2+10x\)

\(=6x-5\)

b) Ta có: \(\left(x+1\right)^2+\left(x-5\right)\left(x+5\right)\)

\(=x^2+2x+1+x^2-25\)

=2x-24

c) Ta có: \(\left(x-3\right)\left(x+3\right)+\left(x-5\right)\left(x+1\right)+\left(x-4\right)^2\)

\(=x^2-9+x^2+x-5x-5+x^2-8x+16\)

\(=3x^2-12x+2\)