1 Descompuneti in factori .
a) ( 3x -4 ) ×( x+7 ) - ( x+7 ) ×( 2x-5) = (x+7)(3x-4-2x+5)=(x+7)(x+1)
b ) 4x² - 49 =(2x-7)(2x+7)
c) 9 × (x+3 )² - 4x² =[3(x+3)-2x][3(x+3)+2x]=(3x+9-2x)(3x+9+2x)=(x+9)(5x+9)
d) 5x²- 10x +5 =5(x²-2x+1)=5(x-1)²
e) a² + 2a + 1 - b² =(a+1)²-b²=(a+1+b)(a+1-b)
Ex 2
Daca a-b =1 , calculati : a² + a - 2ab + b²-b =a² - 2ab + b²+a-b =(a-b)²+(a-b) =1+1=2
Daca a+b =2 , calculati : a²+ b²+ 2a + 2b + 2ab=(a+b)²+2(a+b)=2²+2x2=8