Question

Bài 11 : rút gọn các biểu thức 

a. ( 7x + 4 )² - ( 7x + 4 ) ( 7x - 4 ) 

b. ( x + 2y)² - 6xy ( x + 2y ) 

Bài 12 : Tính 

a. (1/2x + 4)²

b. ( 7x - 5y )²

c. ( 6x² + y² ) ( y² - 6x² ) 

d . ( x + 2y )²

e. ( x - 3y ) ( x + 3y ) 

f. ( 5 - x )²

Answer 1

Bài 12:

a) \(\left(\dfrac{1}{2}x+4\right)^2\)

\(=\left(\dfrac{1}{2}x\right)^2+2\cdot\dfrac{1}{2}x\cdot4+4^2\)

\(=\dfrac{1}{4}x^2+4x+16\)

b) \(\left(7x-5y\right)^2\)

\(=\left(7x\right)^2-2\cdot7x\cdot5y+\left(5y\right)^2\)

\(=49x^2-70xy+25y^2\)

c) \(\left(6x^2+y^2\right)\left(y^2-6x^2\right)\)

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

\(=y^4-36x^4\)

d) \(\left(x+2y\right)^2\)

\(=x^2+2\cdot x\cdot2y+\left(2y\right)^2\)

\(=x^2+4xy+4y^2\)

e) \(\left(x-3y\right)\left(x+3y\right)\)

\(=x^2-\left(3y\right)^2\)

\(=x^2-9y^2\)

f) \(\left(5-x\right)^2\)

\(=5^2-2\cdot5\cdot x+x^2\)

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

Answer 2

\(11,\)

\(a,\left(7x+4\right)^2-\left(7x+4\right)\left(7x-4\right)\)

\(=\left(7x+4\right)\left(7x+4-7x+4\right)\)

\(=\left(7x+4\right).8=56x+32\)

\(b,\left(x+2y\right)^2-6xy\left(x+2y\right)\)

\(=\left(x+2y\right)\left(x+2y-6xy\right)\)

Answer 3

Bài `12`

`(1/2x+4)^2`

`=(1/2x)^2 + 2 . 1/2x.4 + 4^2`

`= 1/4 x^2 +4x + 16`

__

`(7x-5y)^2`

`=(7x)^2-2.7x.5y+(5y)^2`

`= 49x^2 -  70xy   + 25y^2`

__

`(6x^2+y^2)(y^2-6x^2)`

`=(y^2+6x^2)(y^2-6x^2)`

`=(y^2)^2 - (6x^2)^2`

`=y^4-36x^4`

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`(x+2y)^2`

`=x^2+ 2.x.2y+(2y)^2`

`= x^2 + 4xy +4y^2`

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`(x-3y)(x+3y)`

`=x^2 - (3y)^2`

`=x^2 - 9y^2`

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`(5-x)^2`

`=5^2 -2.5.x+x^2`

`=25 - 10x+x^2`

Bài `11`

`(7x+4)^2 -(7x+4)(7x-4)`

`= (7x+4)(7x+4) -(7x+4)(7x-4)`

`=(7x+4)(7x+4-7x+4)`

`=8(7x+4)`

`= 56x+32`

__

`(x+2y)^2-6xy (x+2y)`

`= (x+2y) (x+2y-6xy)`

 

Answer 4

`#040911`

`a,`

\(( 7x + 4 )^2 - ( 7x + 4 ) ( 7x - 4 )\)

`= 49x^2 + 2*7x*4 + 16 - (49x^2 - 16)`

`= 49x^2 + 56x + 16 - 49x^2 + 16`

`= 56x +32`

`b,`

\(( x + 2y)^2 - 6xy ( x + 2y ) \)

`= x^2 + 2*x*2y + 4y^2 - 6x^2y - 12xy^2`

`= x^2 + 4xy + 4y^2 - 6x^2y - 12xy^2`

Answer 5

\(12,\)

\(a,\left(\dfrac{1}{2}x+4\right)^2=\left(\dfrac{1}{2}x\right)^2+2.\dfrac{1}{2}x.4+4^2\)

\(=\dfrac{1}{4}x^2+4x+16\)

\(b,\left(7x-5y\right)^2=\left(7x\right)^2-2.7x.5y+\left(5y\right)^2\)

\(=49x^2-70xy+25y^2\)

\(c,\left(6x^2+y^2\right)\left(y^2-6x^2\right)\)

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

\(=y^4-36x^4\)

\(d,\left(x+2y\right)^2=x^2+2.x.2y+\left(2y\right)^2\)

\(=x^2+4xy+4y^2\)

\(e,\left(x-3y\right)\left(x+3y\right)\)

\(=x^2-9y^2\)

\(f,\left(5-x\right)^2=5^2-2.5.x+x^2\)

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