Bài 1: \(0,125\left(a+1\right)^3-1\)

\(=\left(\frac12a+\frac12\right)^3-1\)

\(=\left(\frac12a+\frac12-1\right)\left\lbrack\left(\frac12a+\frac12\right)^2+\left(\frac12a+\frac12\right)+1^2\right\rbrack\)

\(=\left(\frac12a-\frac12\right)\left(\frac14a^2+\frac12a+\frac14+\frac12a+\frac12+1\right)=\left(\frac12a-\frac12\right)\left(\frac14a^2+a+\frac74\right)\)

BÀi 2:

\(28\cdot122-28\cdot62+30\cdot144\)

\(=28\cdot\left(122-62\right)+60\cdot72\)

\(=60\cdot\left(28+72\right)=60\cdot100=6000\)

Bài 3:

(6x+11)(5x-12)-42x+66=0

=>\(30x^2-72x+55x-132-42x+66=0\)

=>\(30x^2-59x-66=0\)

=>\(x^2-\frac{59}{30}x-\frac{66}{30}=0\)

=>\(x^2-2\cdot x\cdot\frac{59}{60}+\frac{3481}{3600}=\frac{11401}{3600}\)

=>\(\left(x-\frac{59}{60}\right)^2=\frac{11401}{3600}\)

=>\(\left[\begin{array}{l}x-\frac{59}{60}=\frac{\sqrt{11401}}{60}\\ x-\frac{59}{60}=-\frac{\sqrt{11401}}{60}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac{\sqrt{11401}+59}{60}\\ x=\frac{-\sqrt{11401}+59}{60}\end{array}\right.\)

\(\Leftrightarrow30xy-72x+55y-132-42x+16=0\)

\(\Leftrightarrow30xy-72x+55y-42x=0-16+132\)

........................................ Bạn tự làm tiếp nhé!!!

a, 36.28+36.82 +64.69+64.41

=36(28+82)+64(69+41)

=36.110+64.110

=110(36+64)

=110.100

=11000

Hơi mờ

Câu 2 không biết làm

a) 5x + 2x = 6^2 - 5^0

7x = 35

x=5

b) 6x + x = 5^11 : 5^9 + 3^1

7x = 28

x=4

c) 5x + 3x = 3^6 : 3^3 *4 +12

8x = 120

x=15

Lời giải:
a. $(x^2-9)(5x+15)=0$

$\Rightarrow x^2-9=0$ hoặc $5x+15=0$
Nếu $x^2-9=0$

$\Rightarrow x^2=9=3^2=(-3)^2$

$\Rightarrow x=3$ hoặc $-3$
Nếu $5x+15=0$

$\Rightarrow x=-3$
b.

$x^2-8x=0$
$\Rightarrow x(x-8)=0$

$\Rightarrow x=0$ hoặc $x-8=0$

$\Rightarrow x=0$ hoặc $x=8$

c. 

$5+12(x-1)^2=53$

$12(x-1)^2=53-5=48$

$(x-1)^2=48:12=4=2^2=(-2)^2$

$\Rightarrow x-1=2$ hoặc $x-2=-2$
$\Rightarrow x=3$ hoặc $x=0$

d.

$(x-5)^2=36=6^2=(-6)^2$
$\Rightarrow x-5=6$ hoặc $x-5=-6$

$\Rightarrow x=11$ hoặc $x=-1$

e.

$(3x-5)^3=64=4^3$

$\Rightarrow 3x-5=4$

$\Rightarrow 3x=9$

$\Rightarrow x=3$

f.

$4^{2x}+2^{4x+3}=144$
$2^{4x}+2^{4x}.8=144$

$2^{4x}(1+8)=144$

$2^{4x}.9=144$

$2^{4x}=144:9=16=2^4$

$\Rightarrow 4x=4\Rightarrow x=1$

\(\Leftrightarrow x\in\left\{2;-2\right\}\)

\(\Rightarrow\left(x-2\right)\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)

nhấn vào đúng 0 sẽ có câu trả lời

a: \(x^3-9x^2+6x+16\)

\(=x^3-8x^2-x^2+8x-2x+16\)

\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)

\(=\left(x-8\right)\left(x^2-x-2\right)\)

\(=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)

b: \(x^3-x^2-x-2\)

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

\(=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)

\(=\left(x-2\right)\cdot\left(x^2+x+1\right)\)

c: \(x^3+x^2-x+2\)

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

\(=x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-x+1\right)\)

d: \(x^3-6x^2-x+30\)

\(=x^3+2x^2-8x^2-16x+15x+30\)

\(=x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-8x+15\right)\)

\(=\left(x+2\right)\left(x-3\right)\left(x-5\right)\)

e: Sửa đề: \(x^3-7x-6\)

\(=x^3-x-6x-6\)

\(=x\left(x^2-1\right)-6\left(x+1\right)\)

\(=x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+1\right)\left(x-3\right)\left(x+2\right)\)

f: \(27x^3-27x^2+18x-4\)

\(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)

\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)

g: \(2x^3-x^2+5x+3\)

\(=2x^3+x^2-2x^2-x+6x+3\)

\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)

\(=\left(2x+1\right)\left(x^2-x+3\right)\)

h: \(\left(x^2-3\right)^2+16\)

\(=x^4-6x^2+9+16\)

\(=x^4-6x^2+25\)

\(=x^4+10x^2+25-16x^2\)

\(=\left(x^2+5\right)^2-\left(4x\right)^2\)

\(=\left(x^2+5+4x\right)\left(x^2+5-4x\right)\)