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1) \(\left(x+1\right)^2=x^2+2x+1\)
2) \(\left(2x+1\right)^2=4x^2+4x+1\)
3) \(\left(2x+y\right)^2=4x^2+4xy+y^2\)
4) \(\left(2x+3\right)^2=4x^2+12x+9\)
5) \(\left(3x+2y\right)^2=9x^2+12xy+4y^2\)
6) \(\left(2x^2+1\right)^2=4x^4+4x^2+1\)
7) \(\left(x^3+1\right)^2=x^6+2x^3+1\)
8) \(\left(x^2+y^3\right)^2=x^4+2x^2y^3+y^6\)
9) \(\left(x^2+2y^2\right)^2=x^4+4x^2y^2+4y^4\)
10) \(\left(\dfrac{1}{2}x+\dfrac{1}{3}y\right)^2=\dfrac{1}{4}x^2+\dfrac{1}{3}xy+\dfrac{1}{9}y^2\)
a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
a: Ta có: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
b: \(\left(3x+2\right)^2+2\left(3x+2\right)\left(1-2y\right)+\left(1-2y\right)^2\)
\(=\left(3x+2+1-2y\right)^2\)
\(=\left(3x-2y+3\right)^2\)
\(b,\left(x+2\right)^2-25\)
\(=\left(x+2\right)^2-5^2\)
\(=\left(x-3\right)\left(x+7\right)\)
\(c,36\left(x-y\right)^2\)
\(=36\left(x^2-2xy+y^2\right)\)
\(=36x^2-72xy+36y^2\)
\(d,x^2+\dfrac{1}{2}x+\dfrac{1}{16}\)
\(=x^2+2.x.\dfrac{1}{4}+\dfrac{1}{4}^2\)
\(=\left(x+\dfrac{1}{4}\right)^2\)
\(e,2x^4y^3-3x^2y^4+5x^3y^4\)
\(=x^2y^3\left(2x^2-3y+5xy\right)\)
Các câu còn lại làm tương tự, chú ý sd HĐT
Lời giải:
a. $=(x-y)(x+y)=[(-1)-(-3)][(-1)+(-3)]=2(-4)=-8$
b. $=3x^4-2xy^3+x^3y^2+3x^2y+12xy+15y-12xy-12$
$=3x^4-2xy^3+x^3y^2+3x^2y+15y-12$
=3-2.1(-2)^3+1^3.(-2)^2+3.1^2(-2)+15(-2)-12$
$=-25$
c.
$=2x^4+3x^3y-4x^3y-12xy+12xy=2x^4-x^3y$
$=x^3(2x-y)=(-1)^3[2(-1)-2]=-1.(-4)=4$
d.
$=2x^2y+4x^2-5xy^2-10x+3xy^2-3x^2y$
$=(2x^2y-3x^2y)+4x^2+(-5xy^2+3xy^2)-10x$
$=-x^2y+4x^2-2xy^2-10x$
$=-3^2.(-2)+4.3^2-2.3(-2)^2-10.3=0$
Dài rứa :v
Bài 1.
1. ( x + 2y )2 = x2 + 4xy + 4y2
2. ( 2x + 3y )2 = 4x2 + 12xy + 9y2
3. ( 3x - 2y )2 = 9x2 - 12xy + 4y2
4. ( 5x - y )2 = 25x2 - 20xy + y2
5. ( x + 1/4 )2 = x2 + 1/2x + 1/16
6. ( 2x - 1/2 )2 = 4x2 - 2x + 1/4
7. ( 1/3x - 1/2y )2 = 1/9x2 - 1/3xy + 1/4y2
8. ( 3x + 1 )( 3x - 1 ) = ( 3x )2 - 12 = 9x2 - 1
9. ( x2 + 2/5y )( x2 - 2/5y ) = ( x2 )2 - ( 2/5y )2 = x4 - 4/25y2
10. ( x/2 + y )( x/2 - y ) = ( x/2 )2 - y2 = x2/4 - y2
11. Chưa rõ đề
12. \(\left(\sqrt{2x}-y\right)^2=2x-2\sqrt{2x}\cdot y+y^2\)
13. ( 3/2x + 3y )2 = 9/4x2 + 9xy + 9y2
14. \(\left(\sqrt{2x}+\sqrt{8y}\right)^2=2x+\left(2\sqrt{2x}\sqrt{8y}\right)+8y\)
15. ( x + 1/6y + 3 )2 = [( x + 1/6y ) + 3 ]2 = x2 + 1/3xy + 1/36y2 + 6x + y + 9
16. ( 1/2x - 4y )2 = 1/4x2 - 4xy + 16y2
17. ( x/2 + 2y2 )( x/2 - 2y2 ) = ( x/2 )2 - ( 2y2 )2 = x2/4 - 4y4
18. ( x2 - 4 )( x2 + 4 ) = ( x2 )2 - 42 = x4 - 16
19. ( x + y )2 + ( x - y )2 = x2 + 2xy + y2 + x2 - 2xy - y2 = 2x2 + 2y2 = 2( x2 + y2 )
20. ( 2x + 3 )2 - ( x + 1 )2 = [ 2x + 3 + x + 1 ][ 2x + 3 - ( x + 1 )] = [ 3x + 4 ][ x + 2 ]
1. (x + 2y)2 = (x + 2y)(x + 2y) = x(x + 2y) + 2y(x + 2y) = x2 + 2xy + 2xy + 4y2 = x2 + 4xy + 4y2
2. (2x + 3y)2 = (2x + 3y)(2x + 3y) = 2x(2x + 3y) + 3y(2x + 3y) = 4x2 + 6xy + 6xy + 9y2 = 4x2 + 12xy + 9y2
3. (3x - 2y)2 = (3x - 2y)(3x - 2y) = 3x(3x - 2y) - 2y(3x - 2y) = 9x2 - 6xy - 6xy + 4y2 = 9x2 - 12xy + 4y2
4. (5x - y)2 = (5x - y)(5x - y) = 5x(5x - y) - y(5x - y) = 25x2 - 5xy - 5xy - y2 = 25x2 - 10xy - y2
5. (x + 1/4)2 = (x + 1/4)(x + 1/4)
= x(x + 1/4) + 1/4(x + 1/4)
= x2 + 1/4x + 1/4x + 1/16
= x2 + 1/2x + 1/16
6. (2x - 1/2)2 = (2x - 1/2)(2x - 1/2)
= 2x(2x - 1/2) - 1/2(2x - 1/2)
= 4x2 - x - x + 1/4
= 4x2 - 2x + 1/4
7. (1/3x - 1/2y)2 = (1/3x - 1/2y)(1/3x - 1/2y)
= 1/3x(1/3x - 1/2y) - 1/2y(1/3x - 1/2y)
= 1/9x2 - 1/6xy - 1/6xy + 1/4y2
= 1/9x2 - 1/3xy + 1/4y2
8. (3x + 1)(3x - 1)
= 3x(3x - 1) + 1(3x - 1)
= 9x2 - 3x + 3x - 1
= 9x2 - 1
9. \(\left(x^2+\frac{2}{5}y\right)\left(x^2-\frac{2}{5}y\right)\)
= x2(x2 - 2/5y) + 2/5y(x2 - 2/5y)
= x4 - 2/5x2y + 2/5x2y - 4/25y2
= x4 - 4/25y2
10. \(\left(\frac{x}{2}-y\right)\left(\frac{x}{2}+y\right)\)
= \(\frac{x}{2}\left(\frac{x}{2}+y\right)-y\left(\frac{x}{2}+y\right)\)
= \(\frac{x^2+2xy}{4}-\frac{2y^2+xy}{2}\)
= \(\frac{x^2+2xy}{4}-\frac{2\left(2y^2+xy\right)}{4}=\frac{x^2+2xy-4y^2-2xy}{4}\)
= \(\frac{x^2-4y^2}{4}\)
11. Giữ nguyên
Làm nốt đi nhé chứ mỏi tay lắm rồi
Bài 4 : \(\left(x-10\right)^2-x\left(x+80\right)\)
= (x - 10)(x - 10) - x2 - 80x
= x(x- 10) - 10(x - 10) - x2 - 80x
= x2 - 10x - 10x + 100 - x2 - 80x
= (x2 - x2) + (-10x - 10x - 80x) + 100
= -100x + 100 = -100(x - 1)
Thay x = 0,98 vào biểu thức trên ta có :
-100(x - 1) = -100(0,98 - 1) = -100.(-0,02) = 2
2. (2x + 9)2 - x(4x + 31)
= (2x + 9)(2x + 9) - 4x2 - 31x
= 2x(2x + 9) + 9(2x + 9) - 4x2 - 31x
= 4x2 + 18x + 18x + 18 - 4x2 - 31x
= (4x2 - 4x2) + (18x + 18x - 31x) + 18
= 5x + 18
Thay x = -16,2 vào biểu thức trên ta có : 5.(-16,2) + 18 = -63
3. Thay x = 4 vào biểu thức trên ta có :
4.42 - 28.4 + 49 = 4.16 - 112 + 49 = 64 - 112 + 49 = 1
4. Thay x = 1 vào biểu thức trên ta có :
9.12 + 42.1 + 49 = 9 + 42 + 49 = 100
5. Thay x = -1/5 ; y = -5 vào biểu thức trên ta có :
25. (-1/5)2 - 2.(-1/5) . (-5) + 1/25 . (-5)2
= 25 . 1/25 - 2 + 1
= 1 - 2 + 1 = 0
Lần sau đăng ít bài thôi