Question

Me ajudem por favor, são produtos notáveis.

Answer 1

Resposta:

$c)\\ \\ (1+m^{2} )=1^{2} +2*1*m+m^{2} =m^{2} +2m+1\\ \\ d)\\ \\ (x+2)^{2} =x^{2} +2*x*2+2^{2} =x^{2} +4x+4\\ \\ e)\\ \\ (3x+1)^{2} =(3x)^{2} +2*3x*1+1^{2} =9x^{2} +6x+1\\ \\ f)\\ \\ (2y+3)^{2} =(2y)^{2} +2*2y*3+3^{2} =4y^{2} +12y+9\\ \\ g)\\ \\ (a+3b)^{2} =a^{2} +2*a*3b+(3b)^{2} =a^{2} +6ab+9b^{2}$

$h)\\ \\ (4x+3y)^{2} =(4x)^{2} +2*4x*3y+(3y)^{2} =16x^{2} +24xy+9y^{2} \\ \\ i)\\ \\ (a^{2} +7)^{2} =(a^{2} )^{2} +2*a^{2} *7+7^{2} =a^{4} +14a^{2} +49\\ \\ j)\\ \\ (4+x^{2} )^{2} =4^{2} +2*4*x^{2} +(x^{2} )^{2} =x^{4} +8x^{2} +16$

3

$a)\\ \\ (x-3)^{2} =x^{2} -2*x*3+3^{2} =x^{2} -6x+9\\ \\ b)\\ \\ (a-4)^{2} =a^{2} -2*a*4+4^{2} =a^{2} -8a+16\\ \\ c)\\ \\ (5-y)^{2} =5^{2} -2*5*y+y^{2} =y^{2} -10y+25\\ \\ d)\\ \\ (m-6)^{2} =m^{2} -2*m*6+6^{2} =m^{2} -12m+36\\ \\ e)\\ \\ (2x-3)^{2} =(2x)^{2} -2*2x*3+3^{2} =4x^{2} -12x+9$

$f)\\ \\ (a-4b)^{2} =a^{2} -2*a*4b+(4b)^{2} =a^{2} -8ab+16b^{2} \\ \\ g)\\ \\ (5x-3)^{2} =(5x)^{2} -2*5x*3+3^{2} =25x^{2} -30x+9\\ \\ h)\\ \\ (3a-2b)^{2} =(3a)^{2} -2*3a*2b+(2b)^{2} =9a^{2} -12ab+4b^{2}$