A = 4a(a + b)(a + b + c)(a + c) + (bc)²

= 4 × [a(a + b + c)] × [(a + b)(a + c)] + (bc)²

= 4(a² + ab + ac)(a² + ab + ac + bc) + (bc)²

= 4(a² + ab + ac)² + 4bc(a² + ab + ac) + (bc)²

= [2(a² + ab + ac) + bc]² (đpcm)

\begin{aligned}

A &= 4a(a + b)(a + b + c)(a + c) + (bc)^2 \\

&= 4 \times \bigl[a(a + b + c)\bigr] \times \bigl[(a + b)(a + c)\bigr] + (bc)^2 \\

&= 4(a^2 + ab + ac)(a^2 + ab + ac + bc) + (bc)^2 \\

&= 4(a^2 + ab + ac)^2 + 4bc(a^2 + ab + ac) + (bc)^2 \\

&= \bigl[ 2(a^2 + ab + ac) + bc \bigr]^2 \quad \text{(đpcm)}

\end{aligned}

$$

\begin{aligned}

A &= 4a(a + b)(a + b + c)(a + c) + (bc)^2 \\

&= 4 \times \bigl[a(a + b + c)\bigr] \times \bigl[(a + b)(a + c)\bigr] + (bc)^2 \\

&= 4(a^2 + ab + ac)(a^2 + ab + ac + bc) + (bc)^2 \\

&= 4(a^2 + ab + ac)^2 + 4bc(a^2 + ab + ac) + (bc)^2 \\

&= \bigl[ 2(a^2 + ab + ac) + bc \bigr]^2 \quad \text{(đpcm)}

\end{aligned}

$$

$$

\begin{aligned}

A &= 4a(a + b)(a + b + c)(a + c) + (bc)^2 \\

&= 4 \times \bigl[a(a + b + c)\bigr] \times \bigl[(a + b)(a + c)\bigr] + (bc)^2 \\

&= 4(a^2 + ab + ac)(a^2 + ab + ac + bc) + (bc)^2 \\

&= 4(a^2 + ab + ac)^2 + 4bc(a^2 + ab + ac) + (bc)^2 \\

&= \bigl[ 2(a^2 + ab + ac) + bc \bigr]^2 \quad \text{(đpcm)}

\end{aligned}

$$