Question

Calcule usando produtos notáveis:
a) (a-2)²=
b) (a+1)²=
c) (x+2)²=
d) (x+3)²=
e) (a+2).(a-2)=
f) (x+3).(x-3)=

*simplificado*
​

Answer 1

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Quadrado da soma de dois termos

$\huge\boxed{\boxed{\boxed{\boxed{\sf(a+b)^2=a^2+2ab+b^2}}}}$

Quadrado da diferença de dois termos

$\huge\boxed{\boxed{\boxed{\boxed{\sf(a-b)^2=a^2-2ab+b^2}}}}$

Produto da soma pela diferença de dois termos

$\huge\boxed{\boxed{\boxed{\boxed{\sf(a+b)\cdot(a-b)=a^2-b^2}}}}$

$\tt a)~\sf (a-2)^2=(a)^2-2\cdot a\cdot 2+(2)^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf(a-2)^2=a^2-4a+4}}}}\\\tt b)~\sf (a+1)^2=(a)^2+2\cdot a\cdot1+(1)^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf(a+1)^2=a^2+2a+1}}}}\\\tt c)~\sf(x+2)^2=(x)^2+2\cdot x\cdot 2+2^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf(x+2)^2=x^2+4x+4}}}}\\\tt d)~\sf (x+3)^2=(x)^2+2\cdot x\cdot3+(3)^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf(x+3)^2=x^2+6x+9}}}}$

$\tt e)~\sf(a+2)\cdot(a-2)=(a)^2-(2)^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf(a+2)\cdot(a-2)=a^2-4}}}}\\\tt f)~\sf(x+3)\cdot(x-3)=(x)^2-(3)^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf(x+3)\cdot(x-3)=x^2-9}}}}$