Đáp án:

\(\begin{array}{l}
1,\\
a,\,\,\,{y^2} - 8y + 16\\
b,\,\,\,1 + 10a + 25{a^2}\\
c,\,\,\,4{x^2} - 28x + 49\\
d,\,\,{x^2} - \dfrac{2}{3}x + \dfrac{1}{9}\\
e,\,\,\,{x^2} - 36\\
f,\,\,\,4{x^2} - 9\\
2,\\
1.\,\,\,\,{\left( {x + 2} \right)^2}\\
2.\,\,\,\,\left( {t - 1} \right)\left( {t + 1} \right)\\
3.\,\,\,{\left( {4x - 3} \right)^2}\\
4.\,\,\,{\left( {x - 4} \right)^2}\\
5.\,\,\,{\left( {2x + 1} \right)^2}\\
6.\,\,\,\,{\left( {y - \dfrac{1}{2}} \right)^2}\\
3,\\
a,\,\,\,x = 2\\
b,\,\,\,x = 7\\
c,\,\,\,x =  - \dfrac{4}{{11}}\,
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
1,\\
a,\,\,\,{\left( {y - 4} \right)^2} = {y^2} - 2.y.4 + {4^2} = {y^2} - 8y + 16\\
b,\,\,\,{\left( {1 + 5a} \right)^2} = {1^2} + 2.1.5a + {\left( {5a} \right)^2} = 1 + 10a + 25{a^2}\\
c,\,\,\,{\left( {2x - 7} \right)^2} = {\left( {2x} \right)^2} - 2.2x.7 + {7^2} = 4{x^2} - 28x + 49\\
d,\,\,{\left( {x - \dfrac{1}{3}} \right)^2} = {x^2} - 2.x.\dfrac{1}{3} + {\left( {\dfrac{1}{3}} \right)^2} = {x^2} - \dfrac{2}{3}x + \dfrac{1}{9}\\
e,\,\,\,\left( {x - 6} \right)\left( {x + 6} \right) = {x^2} - {6^2} = {x^2} - 36\\
f,\,\,\,\left( {3 + 2x} \right)\left( {2x - 3} \right) = \left( {2x + 3} \right)\left( {2x - 3} \right) = {\left( {2x} \right)^2} - {3^2} = 4{x^2} - 9\\
2,\\
1.\,\,\,\,{x^2} + 4x + 4 = {x^2} + 2.x.2 + {2^2} = {\left( {x + 2} \right)^2}\\
2.\,\,\,\,{t^2} - 1 = {t^2} - {1^2} = \left( {t - 1} \right)\left( {t + 1} \right)\\
3.\,\,\,16{x^2} - 24x + 9 = {\left( {4x} \right)^2} - 2.4x.3 + {3^2} = {\left( {4x - 3} \right)^2}\\
4.\,\,\,{x^2} - 8x + 16 = {x^2} - 2.x.4 + {4^2} = {\left( {x - 4} \right)^2}\\
5.\,\,\,4{x^2} + 4x + 1 = {\left( {2x} \right)^2} + 2.2x.1 + {1^2} = {\left( {2x + 1} \right)^2}\\
6.\,\,\,\,{y^2} - y + \dfrac{1}{4} = {y^2} - 2.y.\dfrac{1}{2} + {\left( {\dfrac{1}{2}} \right)^2} = {\left( {y - \dfrac{1}{2}} \right)^2}\\
3,\\
a,\,\,\,{\left( {3x + 4} \right)^2} = 9x\left( {x - 2} \right) + 100\\
 \Leftrightarrow {\left( {3x} \right)^2} + 2.3x.4 + {4^2}\, = 9{x^2} - 18x + 100\\
 \Leftrightarrow 9{x^2} + 24x + 16 = 9{x^2} - 18x + 100\\
 \Leftrightarrow 9{x^2} + 24x + 16 - 9{x^2} + 18x - 100 = 0\\
 \Leftrightarrow 42x - 84 = 0\\
 \Leftrightarrow 42x = 84\\
 \Leftrightarrow x = 2\\
b,\,\,\,\,\,{\left( {x - 2} \right)^2} - \left( {x + 5} \right)\left( {x - 5} \right) = 1\\
 \Leftrightarrow \left( {{x^2} - 2.x.2 + {2^2}} \right) - \left( {{x^2} - {5^2}} \right) = 1\\
 \Leftrightarrow \left( {{x^2} - 4x + 4} \right) - \left( {{x^2} - 25} \right) = 1\\
 \Leftrightarrow {x^2} - 4x + 4 - {x^2} + 25 - 1 = 0\\
 \Leftrightarrow  - 4x + 28 = 0\\
 \Leftrightarrow 4x = 28\\
 \Leftrightarrow x = 7\\
c,\,\,\,x\left( {x + 9} \right) + 5 = {\left( {x - 1} \right)^2}\\
 \Leftrightarrow {x^2} + 9x + 5 = {x^2} - 2.x.1 + {1^2}\\
 \Leftrightarrow {x^2} + 9x + 5 = {x^2} - 2x + 1\\
 \Leftrightarrow {x^2} + 9x + 5 - {x^2} + 2x - 1 = 0\\
 \Leftrightarrow 11x + 4 = 0\\
 \Leftrightarrow 11x =  - 4\\
 \Leftrightarrow x =  - \dfrac{4}{{11}}\,
\end{array}\)

Đề câu d, e bài 3 bị mất vế phải, em xem lại nhé!