p.19 問2

(1) $$ \begin{align} (a+3)^2 &= a^2+3a\times 2+3^2 \\ &= a^2+6a+9 \end{align}$$
(2) $$ \begin{align} (x-7)^2 &= x^2-7x\times 2+(-7)^2 \\ &= x^2-14x+49 \end{align}$$
(3) $$ \begin{align} (y+4)^2 &= y^2+4y\times 2+4^2 \\ &= y^2+8y+16 \end{align}$$

p.19 問3

(1) $$ \begin{align} (x-5y)^2 &= x^2-5xy\times 2+(-5y)^2 \\ &= x^2-10xy+25y^2 \end{align}$$
(2) $$ \begin{align} (a+4b)^2 &= a^2+8ab+16b^2 \end{align}$$
(3) $$ \begin{align} (4x-y)^2 &= 16x^2-8xy+y^2 \end{align}$$
(4) $$ \begin{align} (2x+3y)^2 &= 4x^2+12xy+9y^2 \end{align}$$
(5) $$ \begin{align} \left(a+\frac{1}{2}b \right)^2 &= a^2+\frac{1}{2}ab\times 2+\left(\frac{1}{2}b \right)^2 \\ &= a^2+ab+\frac{1}{4}b^2 \end{align}$$
(6) $$ \begin{align} (-x+2y)^2 &= (-x)^2-2xy\times 2+(2y)^2 \\ &= x^2-4xy+4y^2 \end{align}$$