Bonjour,
Ex 1
(a+b)²=a²+2ab+b²
(a-b)²=a²-2ab+b²
(a+b)(a-b)=a²-b²
(x+1)²=x²+2x+1
(x-1)²=x²-2x+1
(x+1)(x-1)=x²-1²=x²-1
(2x+1)(2x-1)=4x²-1²=4x²-1
(2x+3)²=4x²+12x+9
(3x-8)²=9x²-48x+64
(3x+5)²+(x-2)²=9x²+30x+25+x²-4x+4=10x²+26x+29
2(2x-4)²+(3x-5)²==2(4x²-16x+16)+9x²-30x+25=8x²-32x+32+9x²-30x+25=17x²-62x+57
(x+4)²-(x+7)²=x²+8x+16-(x²+14x+49)=x²+8x+16-x²-14x-49= -6x-33
Ex 2
(x+5)²=x²+10x+25
(3y+1)²=9y²+6y+1
(a+2)²=a²+4a+4
(2b+3)²=4b²+12b+9
Ex 3
x²-1=(x-1)(x+1)
4x-16xy=4x(1-4y)
(x+8)(x-2)+3(x-2)=(x-2)(x+8+3)=(x-2)(x+11)
(x-1)(x+1)-(x+1)(3x+7)=(x+1)(x-1-3x-7)=(x+1)(-2x-8)
(2x-5)²-3(1-x)(2x-5)=(2x-5)(2x-5-3+3x)=(2x-5)(5x-8)
Et voilà! ;)
