\(x+3y=8\Leftrightarrow x=8-3y\)

 Từ đó \(A=4\left(8-3y\right)^2+y^2\)

\(A=4\left(9y^2-48y+64\right)+y^2\)

\(A=37y^2-192y+256\)

 Đến đây bạn làm tương tự như tìm GTNN của tam thức bậc 2 bình thường nhé.

Mình đang mắc chỗ này, bạn giải tiếp nốt giúp m với

1. My son is crazy about playing computer games

2.Are the students interested in playing games?

3. We are not keen on making models because we are not patient enough

4.We are not interested into cooking because I often cut myself

5.My friends are fond of doing aerobics and they go to the gym every twice a day

6. John likes playing computer games in his free time

7. My brother enjoys playing sports and reading books

8.Juila facies doing DIY when she has free time

9. Everyone adore receiving gifts on their birthday

10. I prefer hanging out with my friends to playing board games

`@` `\text {Ans}`

`\downarrow`

`2,`

`a)`

`-5x^2y^4z^5 (-3xyz^2)`

`= (-5).(-3) . (x^2 . x) . (y^4 . y) . (z^5 . z^2)`

`= 15 x^3 y^5 z^7`

Hệ số: `15`

Phần biến: `x^3 y^5 z^7`

Bậc: `3 + 5 + 7 = 15`

`b)`

`12xy^3z^5 .`\((\dfrac{1}{4}x^3z^3)\)

`=`\((12. \dfrac{1}{4})\)`. (x . x^3) . y^3 . (z^5 . z^3)`

`= 3 x^4 y^3 z^8`

Hệ số: `3`

Phần biến: `x^4y^3z^8`

Bậc: `4+3+8 = 15`

`c)`

\(x^3 . (\dfrac{-5}{4}x^2y)(\dfrac{2}{5}x^3y^4)\)

`=`\(\left(-\dfrac{5}{4}\cdot\dfrac{2}{5}\right)\left(x^3\cdot x^2\cdot x^3\right)\left(y\cdot y^4\right)\)

`=`\(-\dfrac{1}{2}x^8y^5\)

Hệ số: \(-\dfrac{1}{2}\)

Phần biến: `x^8y^5`

Bậc: `8 + 5 = 13`

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

\(=\left(x^2-2\times x\times2+2^2\right)+2x+1\)

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

\(=x^2-4x+4+2x-1\)

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

a) Ta có:

\(x^2-x+1\)

\(=x^2-2\cdot\dfrac{1}{2}\cdot x+\dfrac{1}{4}+\dfrac{3}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)

Mà: \(\left(x-\dfrac{1}{2}\right)^2\ge0\) và \(\dfrac{3}{4}>0\) nên

\(\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\forall x\)

\(\Rightarrow x^2-x+1>0\forall x\)

1.

$3x^4-48=3(x^4-16)=3[(x^2)^2-4^2]=3(x^2-4)(x^2+4)$

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

2. 

$x^3-4x^2+8x-8=(x^3-8)-(4x^2-8x)$
$=(x-2)(x^2+2x+4)-4x(x-2)=(x-2)(x^2+2x+4-4x)=(x-2)(x^2-2x+4)$

3.

$x^4-27x=x(x^3-27)=x(x^3-3^3)=x(x-3)(x^2+3x+9)$

4.

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

$=(x-1)(x^3+x+1)$

5.

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

6.

$x^3+2x^2+2x+1=(x^3+x^2)+(x^2+2x+1)=x^2(x+1)+(x+1)^2$
$=(x+1)(x^2+x+1)$

7.

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

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

8.

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

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

Lời giải:

a. $A=3xy(x^2+2xy+y^2)=3xy(x+y)^2=3.\frac{1}{2}.\frac{-1}{3}(\frac{1}{2}+\frac{-1}{3})^2=\frac{-1}{72}$

b. 

$B=(-1)^2.3^2+(-1).3+(-1)^3+3^3=32$

c.

$D=5^2+4.5.1-3.1^3=42$

d.

$D=2xy(x+y)=2.1(-3)(1-3)=12$

e. 

$M=\frac{(x+2)(2x-1)}{x+2}=2x-1=2(-1)-1=-3$