Question

GENTE EU IMPLORO A AJUDA DE VOCÊS POR FAVOR!!!!!!! EU IMPLORO
1 – Desenvolva o quadrado da soma de dois termos:
a) (a + 7)2 =
b) (3x + 1)2 =
c) (5 + 2m)2 =
d) (a + 3x)2 =
e) (5x2 + 1)2 =
f) (c3 + 6)2 =
g) (10 + a)2 =
h) (x2 + x)2 =
i) (a5 + c4 ) 2 =
j) (3m2 + 4n)2 =
2 – Desenvolva o quadrado da diferença de dois termos:
a) (m – 3)2 =
b) (2a – 5)2 =
c) (7 –3c)2 =
d) (4m2 – 1)2 =
e) (2 – x 3 ) 2 =
f) (a3 – 3c2 ) 2 =
g) (5a – 3)2 =
h) (p5 – 10)2 =
i) (3m2 – a)2 =
j) ( a5 – c 3 ) 2 =
3 – Desenvolva o produto da soma pela diferença de dois termos:
a) (x + 9).(x – 9) =
b) (m – 1).(m + 1) =
c) (3x + 5).(3x - 5) =
d) (2 – 7x).(2 + 7x) =
e) ( m2 – 5). (m2 + 5) =
f) (p3 + 3).(p3 – 3) =
g) (2a + 5).(2a – 5) =
h) (1 – x 5 ). (1 + x5 ) =
i) (a2 + b3 ). (a2 – b 3 ) =
j) (m2 – n 5 ). (m2 + n5 ) =
4 – Desenvolva o cubo da soma de dois termos:
a) (x + 2)3 =
b) (2x + 1)3 =
c) (1 + x2 ) 3 =
d) (x2 + 2)3 =
e) (2 + 3z 2 ) 3 =
5 – Desenvolva o cubo da diferença de dois termos:
a) (a – 1)3 =
b) (2x – 3)3 =
c) (2a – b)3 =
d) (1 – 3a2 ) 3 =
e) ( 5 – x)3 =
6 – Fatore as seguintes expressões :
I)
a) 6x3 + 8x2
b) 14xy – 21xz
c) 33xy2 - 44x2y + 22x2y
d) 4ax2 + 6a2x2 + 4a3x2
II)
a) y3 - 5y2 + y - 5
b) 2x + ay + 2y + ax
c) y3 - 3y2 + 4y - 12
d) ax2 - bx2 + 3a – 3b
III)
a) x2 - 10x + 25
b) 16x2 + 24xy + 9y2
c) 3x2 + 6x + 3
d) 25a 4 – 100b2
e) (ab + a2) (ab – a2)
IV)
a) x2 - y2
b) a2b4 - 9
c) 16 – 4x2
d) 1000 – x2y2
e) y2 - 1

Answer 1

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1)

$\tt a)~\sf(a+7)^2=a^2+14a+49\\\tt b)~\sf(3x+1)^2=9x^2+6x+1\\\tt c)~\sf(5+2m)^2=25+20m+4m^2\\\tt d)~\sf(a+3x)^2=a^2+6ax+9x^2\\\tt e)~\sf(5x^2+1)^2=25x^4+10x^2+1\\\tt f)~\sf(c^3+6)^2=c^6+12c^3+36\\\tt g)~\sf(10+a)^2=100+20a+a^2\\\tt h)~\sf h)(x^2+x)^2=x^4+2x^3+x^2\\\tt i)~\sf(a^5+c^4)^2=a^{10}+2a^5c^4+c^8\\\tt j)~\sf(3m^2+4n)^2=9m^4+24m^2n+16n^2$

2)

$\tt a)~\sf(m-3)^2=m^2-6m+9\\\tt b)~\sf(2a-5)^2=4a^2-20a+25\\\tt c)~\sf(7-3c)^2=49-42c+9c^2\\\tt d)~\sf(4m^2-1)^2=16m^4-8m^2+1\\\tt e)~\sf(2-x^3)^2=4-4x^3+x^6\\\tt f)~\sf(a^3-3c^2)^2=a^6-6a^3c^2+9c^4\\\tt g)~\sf(5a-3)^2=25a^2-30a+9\\\tt h)~\sf(p^5-10)^2=p^{10}-10p^5+100\\\tt i)~\sf(3m^2-a)^2=9m^4-6m^2a+a^2\\\tt j)~\sf(a^5-c^3)^2=a^{10}-2a^5c^3+c^6$

3)

$\tt a)~\sf(x+9)(x-9)=x^2-81\\\tt b)~\sf(m-1)(m+1)=m^2-1\\\tt c)~\sf(3x+5)(3x-5)=9x^2-25\\\tt d)~\sf(2-7x)(2+7x)=4-49x^2\\\tt e)~\sf(m^2-5)(m^2+5)=m^4-25\\\tt f)~\sf (p^3+3)(p^3-3)=p^6-9\\\tt g)~\sf(2a+5)(2a-5)=4a^2-25\\\tt h)~\sf(1-x^5)(1+x^5)=1-x^{10}\\\tt i)~\sf(a^2+b^3)(a^2-b^3)=a^4-b^6\\\tt j)~\sf(m^2-n^5)(m^2+n^5)=m^4-n^{10}$

4)

$\tt a)~\sf(x+2)^3=x^3+6x^2+12x+8\\\tt b)~\sf(2x+1)^3=8x^3+12x^2+6x+1\\\tt c)~\sf(1+x^2)^3=1+3x^2+3x^4+x^6\\\tt d)~\sf(x^2+2)^3=x^6+6x^4+12x^2+8\\\tt e)~\sf(2+3z^2)^3=8+36z^2+54z^4+27z^6$

5)

$\tt a)~\sf(a-1)^3=a^3-3a^2+3a-1\\\tt b)~\sf(2x-3)^3=8x^3-36x^2+54x-27\\\tt c)~\sf(2a-b)^3=8a^3-12a^2b+6ab^2-b^3\\\tt d)~\sf(1-3a^2)^3=1-9a^2+27a^4-27a^6\\\tt e)~\sf(5-x)^3=125-75x+15x^2-x^3$

6)

I

$\tt a)~\sf6x^3+8x^2=2x^2(3x+4)\\\tt b)~\sf14xy-21xz=7x(2y-3z)\\\tt c)~\sf33xy^2-44x^2y+22x^2y=33xy^2-22x^2y\\\sf=11xy(3y-2x)\\\tt d)~\sf 4ax^2+6a^2x^2+4a^3x^2=2ax^2(2+3a+2a^2)$        

II

$\tt a)~\sf y^3-5y^2+y-5=y^2(y-5)+1(y-5)\\\sf =(y-5)\cdot(y^2+1)\\\tt b)~\sf 2x+ay+2y+ax=2x+2y+ax+ay\\\sf =2\cdot(x+y)+a\cdot(x+y)=(a+2)\cdot(x+y)\\\tt c)~\sf y^3-3y^2+4y-12=y^2(y-3)+4\cdot(y-3)\\\sf =(y-3)(y^2+4)\\\tt d)~\sf ax^2-bx^2+3a-3b=x^2(a-b)+3(a-b)\\\sf =(a-b)(x^2+3)$

III

$\tt a)~\sf x^2-10x+25=(x-5)^2\\\tt b)~\sf16x^2+24xy+9y^2=(4x+3y)^2\\\tt c)~\sf3x^2+6x+3=3\cdot(x^2+2x+1)=3\cdot(x+1)^2\\\tt d)~\sf 25a^4-100b^2=(5a^2-10b)(5a^2+10b)\\\tt e)~\sf(ab+a^2)(ab-a^2)=a^2b^2-a^4\\\sf =a^2(b^2-a^2)=a^2(b-a)(b+a)$

IV

$\tt a)~\sf x^2-y^2=(x-y)(x+y)\\\tt b)~\sf a^2b^4-9=(ab-3)(ab+3)\\\tt c)~\sf16-4x^2=(4-2x)(4+2x)\\\tt d)~\sf1000-x^2y^2=(10\sqrt{10}-xy)(10\sqrt{10}+xy)\\\tt e)~\sf y^2-1=(y-1)(y+1)$