Question

3. Descompuneti in factori, folosind metoda factorului comun:
a) a(x+y)+a(b-x)
c) 2c(a+b)+c(5a-3b)
e) a(b+c)+x(b+c)
g) x(2x+3)-3(2x+3)
i) 2x(m-n)-(n-m)

4. Descompuneti in factori, folosind metoda gruparii:
a) ax+bx+ac+bc
d) 6x+7y+42+xy

5. Descompuneti in factori, folosind metoda gruparii:
a)2a+b+2a^2+ab
c) 2x^2-3x+4ax-6a
e) ab+ac+am+yb+yc+ym

6. Descompuneti in factori, folosind formule de calcul prescurtat:
a) 4a^2+4ab+b^2
d) 9/16a^2-2ab+16/9b^2
g) 4+0,25x^2-2x

7.Descompuneti in factori:
a) 4x^2-1
e) -n^2+b^2
i) 49x^2-121a^2



DAU 100 DE PUNCTE SI COROANA!!!

Answer 1

La ex6 folosim formula a^2-2ab+b^2=(a-b)^2 iar la 7 a^2-b^2=(a-b)(a+b)

Answer 2

3)

a)   a ( x + y ) + a ( b - x ) = a × ( x + y + b - x ) = a × ( y + b )

c)   2 c ( a + b ) + c ( 5 a - 3 b ) = c × ( 2 a + 2 b + 5 a - 3 b ) = c × ( 7 a - b )

e)   a ( b + c ) + x ( b + c ) = ( b + c ) ( a + x )

g)  x ( 2 x + 3 ) - 3 ( 2 x + 3 ) = ( 2 x + 3 )  ( x - 3 )

i)    2 X ( m - n ) - ( n - m ) =

= 2 X ( m - n ) - n + m =

= 2 X ( m - n ) + ( m - n ) =

= ( m - n ) ( 2 X + 1 )

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4)

a)    a x + b x + a c + b c = a ( x + c ) + b ( x + c ) = ( x + c ) ( a + b )

d)    6 x + 7 y + 42 + x y =

= 6 ( x + 7 ) + y ( 7 + x ) =

= ( x + 7 ) ( 6 + y )    

→ adunarea este comutativa 7 + x = x + 7

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5)

a)  2 a + b + 2 a² + a b = 2 a ( 1 + a ) + b ( 1 + a ) = ( 1 + a ) ( 2 a + b )

sau:  = ( a + 1 ) ( 2 a + b )

c)    2 x² - 3 x + 4 a x - 6 a =  ( x + 2 a ) ( 2 x - 3 )

= 2 x ( x + 2 a ) - 3 ( x + 2 a ) =

= ( x + 2 a ) ( 2 x - 3 )

e)  

ab + ac + am + yb + yc + ym = ( a + y ) ( b + c + m )

= b ( a + y ) + c ( a + y ) + m ( a + y ) =

= ( a + y ) ( b + c + m )

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6)

a)  4 a² + 4 ab + b² = ( 2 a + b ) ² = ( 2 a + b ) ( 2 a + b )

sau:

=  4 a² + 2 ab + 2 ab + b² =

= 2 a ( a + b ) + b ( 2 a + b ) =

= (2 a + b ) ( 2 a + b )

d)

( 9 / 16)  a² - 2 a b + ( 16 / 9 ) b² =  ( 3 a / 4 + 4 b / 3 ) ( 3 a / 4 - 4 b / 3 )

→ aplic formula  a² - b² = ( a - b ) ( a + b )

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g)  

4 + 0,25² - 2 x = ( 0,5 x - 2 ) ( 0,5 x + 2 )

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7)  

a) 4 x² - 1 = ( 2 x - 1 ) ( 2 x + 1 )

e)     b² - n² = ( b + n ) ( b - n )

i)     49 x² - 121 a² = ( 7 x - 11 a ) ( 7 x + 11 a )