Respostas

  • Usuário do Brainly
2014-08-23T15:49:34-03:00
A) 3x^2-15x=\boxed{3x(x-5)}.

b) 5a^2-a+10ab-2b=a(5a-1)+b(5a-1)=\boxed{(a+b)(5a=1)}

c) x^2+40x+400=x^2+2\cdot20\cdot x+20^2=\boxed{(x+20)^2}

d) 9x^2-25=(3x)^2-5^2=\boxed{(3x+5)(3x-5)}

e) 16a^2-8a+1=(4a)^2-2\cdot4a\cdot1+1^2=\boxed{(4a-1)^2}

f) r^2-2rs+s^2=\boxed{(r-s)^2}

g) m^2-n^2=\boxed{(m+n)(m-n)}

h) 49x^2-144y^2=(7x)^2-(12y)^2=\boxed{(7x+12y)(7x-12y)}

56) 

a) x^2-1=x^2-1^2=\boxed{(x+1)(x-1)}

b) y^2-81=y^2-9^2=\boxed{(y+9)(y-9)}

c) 1-a^2=1^2-a^2=\boxed{(1+a)(1-a)}

d) x^2-144=x^2-12^2=\boxed{(x+12)(x-12)}

e) 36-\dfrac{x^2}{49}=6^2-\left(\dfrac{x}{7}\right)^2=\left(6+\dfrac{x}{7}\right)(6-\dfrac{x}{7}\right)

57) (x+13)(x-13)=x^2-13x+13x-169=\boxed{x^2-169}

Helen não acertou, porque (x+13)(x-13)\ne x^2+169

59)
a) 45x^2-5xy^2=5x(9x^2-y^2)=\boxed{5x(3x+y)(3x-y)}

b) a^4-b^4=(a^2)^2-(b^2)^2=(a^2-b^2)(a^2+b^2)=\boxed{(a+b)(a-b)(a^2+b^2)}

c) xy - 5x + 4y - 20 = x(y - 5)+4(y-5)=\boxed{(x+4)(y-5)}

d) y^3-9y=y(y^2-9)=y(y^2-3^2)=\boxed{y(y+3)(y-3)}

e) x^2+2xy+y^2+5x+5y=(x+y)(x+y)+5(x+y)=\boxed{(5+x+y)(x+y)}

f) a^2-3a-ab+3b=a(a-b)-3(a-b)=\boxed{(a-3)(a-b)}


60) 

a)

108^2=(100+8)^2=100^2+2\cdot100\cdot8+8^2=10~000+1~600+64=11~664

b)

999^2=(1~000-1)^2=1~000^2-2\cdot1~000\cdot1+1^2=1~000~000-2~000+1=998~001

c)

1~001^2+999^2=(1~000+1)^2+998~001=1~000~000+2~000+1+998~001=2~000~002

d)

105^2-95^2=(105+95)(105-95)=200\cdot10=2~000

e)

100~001^2-99~999^2=(100~001+99~999)(100~001-99~999)=200~000\cdot2=400~000

f)

9~999^2=(10~000-1)^2=10~000^2-2\cdot10~000+1^2=100~000~000-20~000+1=99~980~001