Question

Calcule a soma ou a diferença de quadrados.

A) (a + b)² =

B) (a - b)² =

C) (2 a + 3b)² =

D) (2 a - 3b)² =

E) (x + y )² - y² =​

Answer 1

Explicação passo-a-passo:

a)

$\sf (a+b)^2=a^2+2\cdot a\cdot b+b^2$

$\sf (a+b)^2=a^2+2ab+b^2$

b)

$\sf (a-b)^2=a^2-2\cdot a\cdot b+b^2$

$\sf (a-b)^2=a^2-2ab+b^2$

c)

$\sf (2a+3b)^2=(2a)^2+2\cdot2a\cdot3b+(3b)^2$

$\sf (2a+3b)^2=4a^2+12ab+9b^2$

d)

$\sf (2a-3b)^2=(2a)^2-2\cdot2a\cdot3b+(3b)^2$

$\sf (2a-3b)^2=4a^2-12ab+9b^2$

e)

$\sf (x+y)^2-y^2=(x+y-y)\cdot(x+y+y)$

$\sf (x+y)^2-y^2=x\cdot(x+2y)$

$\sf (x+y)^2-y^2=x^2+2xy$