Question

simplifique as seguintes expressoes algebricas:
a) 5y² - (-4y² + 7y²) + (-y² +9y² - 11y²)
b) ( a - b)² - (a + b) (a - b)
c) (2x - y)² + (x + y)(x - y)
d) (a + x)² - 2ax + -( x - a ) (x + a)
e) ( a x b)² - ( a - b )² - 4ab
f) ( m + n )² - 2mn + (n - m) (n + m)
g) ( a - b³) ( a + b³) + (b² + a ) ( b² - a )
h) ( 2x - 3y)² + ( 2 x + 3y)² - ( 2x + 3y) (2x - 3y)
i) ( x + 2)² + ( x + 1)²
j) ( x - 3)² + x( x + 2)² - x³
k) ( a + 3)² - ( a - 5)² + 2a( a - 7)

Answer 1

Resposta:

Explicação passo a passo:

A)5y² -(-4y² + 7y²) + (-y² + 9y² - 11y²) =

5y² + 4y² - 7y² - y² + 9y² -11y² =

y²(5 + 4 -7 -1 + 9 -11) = -y

B)(a-b)² -(a+b)(a-b)

a²-2ab+b²- (a²-b²)

a²-2ab+b²-a²+b²

a²-a²-2ab+b²+b²

-2ab+2b²

C) (2x-y)2+(x+y).(x-y)

(2x-y)2+ x2-xy+yx+y2

2x2-y2+x2-x2+y2+y2

2x2+x+y6

2x3+y6

D) (a+x)²-2ax+(x-a)(x+a) =

a² + 2a.x +  x² - 2ax +  x² - a² = 0

E)  (a+b)² - (a-b)² - 4ab

(a)² -2(a)(b) +(b)² -(a² -2(a)(b) +b²) -4ab

a² -2ab +b² -(a² -2ab +b²) -4ab

a² -2ab +b² -a² +2ab +b² -4ab

a²-a² -2ab +2ab -4ab +b² +b²

-4ab +2b²

a²-a² -2ab +2ab

F)(m+n)² -2mn + (n-m)(n-m)

(m)² + 2(m)(n) +(n)²  +(n²  -mn -mn +m² )

m²  +2mn +n²  +(n²  -2mn +m² )

m²  +2mn +n²  +n² -2mn +m²

m²  +m²  +2mn-2mn+n²  +n²

2m² +2n²

+2mn-2mn

G)(a-b³)(a+b³) + (2x + 3y)(2x-3y)

(a² +ab³ -ab³ -b⁶) +( 4x² -6xy +6xy-9y²)

a² +ab³ -ab³ -b⁶  +4x² -6xy +6xy-9y²

a² - b⁶ +4x²-9y²

+ab³ -ab³ e -6xy +6xy

H) (2x - 3y)² = (2x - 3y)(2x - 3y) = 4x²-6xy-6xy+9y² = (4x²-12xy+9y²)

(2x + 3y)² = (2x + 3y)(2x + 3y) = 4x²+6xy+6xy+9y² = (4x²+12xy+9y²)

(2x + 3y)(2x - 3y) = 4x²-6xy+6xy-9y² = (4x²-9y²)

(2x - 3y)² + (2x + 3y)² - (2x + 3y)(2x - 3y)

(4x²-12xy+9y²) + (4x²+12xy+9y²) - (4x²-9y²)

4x²-12xy+9y² + 4x²+12xy+9y² - 4x²+9y²

4x²+4x²-4x² -12xy+12xy +9y²+9y²+9y²

4x²+4x²-4x²=4x²

-12xy+12xy=0

9y²+9y²+9y²=27y²

4x²+0+27y²

4x²+27y²

I)(x + 1)² + (x + 2)² =

x² + 2 · x · 1 + 1² + x² + 2 · x · 2 + 2² =

x² + 2x + 1 + x² + 4x + 4 =

2x² + 6x² + 5

J) (x-3)²+x(x+2)²-x³ =

(x² -6x + 9) + x(x² + 4x + 4) - x³

x² - 6x+9 + x³ + 4x² + 4x - x³

4x² + x² - 6x + 4x - x³ + x³ + 9

5x² - 2x +9

=5x² - 2x + 9

K) a² + 9 - A² - 25 + 2A² - 14

a² + 9 - 25 - 14 - A² + 2A²

a² - 30 - 3A²