Question

01. Calcule os quadrados:
a) (3x + 1)2 =
c) ( 23 - 3c)2 =
b) (x10+ 4 )2 =
d) (5a - 3)2 =
02. Simplifique as expressões:
a) (x+1)++ (x+ 5)2 =
c) ( 3x - 1)2 + (x - 2)2 =
b) (x+y)2 -2C x2 + y2 ) =
d) (1 - 2x)2 - (1 + x)2 =
e) (x+3)(x-3)+(x - 3)2 =
03. Calcule os produtos:
a) (x+9). (x - 9) =
b) (xy + 4). (xy - 4) =
c) ( 5x2 - y2) ( 5x2 - y2) =​

Answer 1

Resposta:

01)

a)

$(a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} \\ \\ (3x + 1) {}^{2} = (3x) {}^{2} + 2(3x)(1) + {(1)}^{2} \\ \\ = \Large \boxed{ \green{ 9 {x}^{2} + 6x + 1}}$

c)

$(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2} \\ \\ (23 - 3c) {}^{2} = {(23)}^{2} - 2(23)(3c) + {(3c)}^{2} \\ \\ = \Large \boxed{ \green{529 - 138c + 9 {c}^{2} }}$

b)

$({x}^{10} + 4) {}^{2} =( {x}^{10}) {}^{2} + 2( {x}^{10} )(4) + {4}^{2} \\ \\ = \Large \boxed{ \green{ {x}^{20} + 8 {x}^{10} + 16}}$

d)

$(5a - 3) {}^{2} = (5a) {}^{2} - 2(5a)(3) + {3}^{2} \\ \\ = \Large \boxed{ \green{ 25 {a}^{2} - 30a + 9}}$

02)

a)

$(x + 1) + (x + 5) {}^{2} = \\ \\ = x + 1 + {x}^{2} + 2(x)(5) + {5}^{2} \\ \\ = x + 1 + {x}^{2} + 10x + 25 \\ \\ = \Large \boxed{ \green{ {x}^{2} + 11x + 26}}$

c)

$(3x - 1) {}^{2} + (x - 2) {}^{2} = \\ \\ = (3x) {}^{2} - 2(3x)(1) + {1}^{2} + {x}^{2} - 2(x)(2) + {2}^{2} \\ \\ = 9 {x}^{2} - 6x + 1 + {x}^{2} - 4x + 4 \\ \\ = \Large \boxed{ \green{10 {x}^{2} - 10x + 5}}$

b)

$(x + y) {}^{2} - 2( {x}^{2} + {y}^{2} ) = \\ \\ = {x}^{2} + 2xy + {y}^{2} - 2 {x}^{2} - 2 {y}^{2} \\ \\ = \Large \boxed{ \green{ - {x}^{2} + 2xy - {y}^{2} }}$

d)

$(1 - 2x) {}^{2} - (1 + x) {}^{2} = \\ \\ = {1}^{2} - 2(1)(2x) + ( {2x)}^{2} - ( 1 + 2x + {x}^{2} ) \\ \\ \red 1 - 4x + 4 {x}^{2} \red{ - 1} - 2x - {x}^{2} \\ \\ = \Large \boxed{ \green{- 3 {x}^{2} - 6x}}$

e)

$(x + 3)(x - 3) + (x - 3) {}^{2} = \\ \\ = {x}^{2} - (3) {}^{2} + {x}^{2} - 2(x)(3) + {3}^{2} \\ \\ = {x}^{2} \red{ - 9} + {x}^{2} - 6x \red{ + 9 }\\ \\ = \Large \boxed{ \green{2 {x}^{2} - 6x}}$

3)

a)

$(x + 9)(x - 9) = {x}^{2} - {9}^{2} = \\ \\ = \Large \boxed{ \green{ {x}^{2} - 81}}$

b)

$(xy + 4)(xy - 4) = \\ \\ (xy) {}^{2} - {4}^{2} = \\ \\ = \Large \boxed{ \green{ {x}^{2} {y}^{2} - 16}}$

c)

$(5 {x}^{2} - {y}^{2} )(5 {x}^{2} - {y}^{2} ) = \\ \\ (5 {x}^{2} ) {}^{2} - ( {y}^{2} ) {}^{2} = \\ \\ = \Large\boxed{ \green{5 {x}^{4} - {y}^{4} }} \\ \\ \Large \boxed{ \underline{ \blue{ \bf \: Bons \: Esudos!}11/05/2021}}$