Vamos calcular a expressão:

( 500 2 + 600 2 + 700 2 + 800 2 + 900 2 ) − ( 499 2 + 599 2 + 699 2 + 799 2 + 899 2 ) (500 2 +600 2 +700 2 +800 2 +900 2 )−(499 2 +599 2 +699 2 +799 2 +899 2 ) Passo 1: Usar a diferença de quadrados Para cada par 𝑎 2 − 𝑏 2

( 𝑎 − 𝑏 ) ( 𝑎 + 𝑏 ) a 2 −b 2 =(a−b)(a+b).

Vamos calcular para cada termo:

500 2 − 499 2

( 500 − 499 ) ( 500 + 499 )

1 × 999

999 500 2 −499 2 =(500−499)(500+499)=1×999=999

600 2 − 599 2

1 × ( 600 + 599 )

1 × 1199

1199 600 2 −599 2 =1×(600+599)=1×1199=1199

700 2 − 699 2

1 × ( 700 + 699 )

1 × 1399

1399 700 2 −699 2 =1×(700+699)=1×1399=1399

800 2 − 799 2

1 × ( 800 + 799 )

1 × 1599

1599 800 2 −799 2 =1×(800+799)=1×1599=1599

900 2 − 899 2

1 × ( 900 + 899 )

1 × 1799

1799 900 2 −899 2 =1×(900+899)=1×1799=1799

Passo 2: Somar as diferenças 999 + 1199 + 1399 + 1599 + 1799 999+1199+1399+1599+1799 Calculando:

999 + 1199

2198 999+1199=2198 2198 + 1399

3597 2198+1399=3597 3597 + 1599

5196 3597+1599=5196 5196 + 1799

6995 5196+1799=6995 Resposta correta: a) 6995