Question

1 – Desenvolva os produtos notáveis: a) ( m + 4 )2 = b) ( 8x – 1)2 = c) ( 10x – 1)2 = d) ( 5x + 2y)2 = 2 – Fatore por agrupamento: a) ax + bx + ac + bc = b) dm + dp + 7m + 7p = 3 – Fatore as diferenças: a) x2 – 25 = b) m4 – 64 = c) d2 - 49 = d) x2 – 100 = 4 – Fatore os trinômios: a) x2 + 10x + 25 = b) x2 + 16x + 64 = 5 – Simplifique: ( 9x)2 + ( 11 + 9x).(11 – 9x) = (18x) + (20x).(1x)= 6 – Fatore os produtos: a) ( x + 7).(x – 7 ) = b) (m +10).(m – 10 ) =

Answer 1

1.

a) $(m+4)^2=m^2+2\cdot m\cdot4+4^2$

$(m+4)^2=m^2+8m+16$

b) $(8x-1)^2=(8x)^2-2\cdot8x\cdot1+1^2$

$(8x-1)^2=64x^2-16x+1$

c) $(10x-1)^2=(10x)^2-2\cdot10x\cdot1+1^2$

$(10x-1)^2=100x^2-20x+1$

d) $(5x+2y)^2=(5x)^2+2\cdot5y\cdot2y+(2y)^2$

$(5x+2y)^2=25x^2+20xy+4y^2$

2.

a) $ax+bx+ac+bc=x\cdot(a+b)+c\cdot(a+b)$

$ax+bx+ac+bc=(a+b)\cdot(x+c)$

b) $dm+dp+7m+7p=d\cdot(m+p)+7\cdot(m+p)$

$dm+dp+7m+7p=(m+p)\cdot(d+7)$

3.

a) $x^2-25=x^2-5^2$

$x^2-25=(x-5)\cdot(x+5)$

b) $m^4-64=(m^2)^2-8^2$

$m^4-64=(m^2-8)\cdot(m^2+8)$

c) $d^2-49=d^2-7^2$

$d^2-49=(d-7)\cdot(d+7)$

d) $x^2-100=x^2-10^2$

$x^2-100=(x-10)\cdot(x+10)$

4.

a) $x^2+10x+25=x^2+5x+5x+25$

$x^2+10x+25=x\cdot(x+5)+5\cdot(x+5)$

$x^2+10x+25=(x+5)\cdot(x+5)$

$x^2+10x+25=(x+5)^2$

b) $x^2+16x+64=x^2+8x+8x+64$

$x^2+16x+64=x\cdot(x+8)+8\cdot(x+8)$

$x^2+16x+64=(x+8)\cdot(x+8)$

$x^2+16x+64=(x+8)^2$

5.

a) $(9x)^2+(11+9x)\cdot(11-9x)=81x^2+11^2-(9x)^2$

$(9x)^2+(11+9x)\cdot(11-9x)=81x^2+121-81x^2$

$(9x)^2+(11+9x)\cdot(11-9x)=121$

b) $18x+20x\cdot x=18x+20x^2$

$18x+20x\cdot x=2x\cdot(9+10x)$

6.

a) $(x+7)\cdot(x-7)=x^2-7^2$

$(x+7)\cdot(x-7)=x^2-49$

b) $(m+10)\cdot(m-10)=m^2-10^2$

$(m+10)\cdot(m-10)=m^2-100$