Question

Fatores os trinomios quadrados perfeitos.

$A) 4x^2+12x+9\\\\B) x^2-14x+49\\\\C) y^2+2y+1\\\\D) a^2-20a+100\\\\E) 1+2x+x^2\\\\F) m^2-12m+36\\\\G) 9x^2+12x+4\\\\H) 4m^2-20m+25\\\\I)x^2-18x+81\\\\J) 16y^2-8y+1\\\\K) 9x^2+36xy+36y^2\\\\L) 25a^2+60ab+36b^2$

Answer 1

$\textbf{ a) ( 2x + 3 )^2 \emph}$

$\textbf{b) ( x + 7 )^2 \emph}$

$\textbf{c) ( y + 1 )^2 \emph}$

$\textbf{d) ( a + 10 )^2 \emph}$

$\textbf{e) ( x + 1 )^2 \emph}$

$\textbf{f) ( m - 6 )^2 \emph}$

$\textbf{g) ( 3x + 2 )^2 \emph}$

$\textbf{h) ( 2m +5 )^2 \emph}$

$\textbf{i) ( x + 9 )^2 \emph}$

$\textbf{ j) ( 4y - 1 )^2 \emph}$

$\textbf{k) 9 . ( x + 2 )^2 \emph}$

$\\\ \textbf{l) ( 5a + 6b )^2 \emph}$

            Fatoração trinômios quadrados perfeitos

• Para expandir qualquer binômio, podemos aplicar um dos seguintes modelos.

$(a+ b)^2=a^2+2ab + b^2\\ \\ (a- b)^2 = a^2 - 2ab + b^2$

• O inverso deste processo de expansão é uma forma de fatoração. Se reescrevermos as equações na ordem inversa, nós teremos modelos para a fatoração de polinômios da forma  $a^2\pm2ab+b^2$

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$a)\\\\ 4x^2 + 12x + 9\\\\ ( 2x + 3) . ( 2x + 3) \\\\ \textbf{ ( 2x + 3)^2 \emph}$

$b)\\\\ x^2 + 14x + 49\\\\ ( x + 7) . ( x + 7 \\\\ \textbf{ ( x + 7)^2 \emph}$

$c)\\\\ y^2 + 2y + 1\\\\ ( y + 1) . ( y + 1) \\\\ \textbf{ ( y + 1)^2 \emph}$

$d)\\\\ a^2 +20a = 100\\\\ ( a + 10) . ( a + 10) \\\\ \textbf{ ( a + 10)^2 \emph}$

$e)\\\\ 1 + 2x + x^2\\\\ ( x + ') . ( x + ') \\\\ \textbf{ ( x + 1)^2 \emph}$

$f)\\\\ m^2 - 12m + 36\\\\ ( m - 6) . ( m - 6) \\\\ \textbf{ ( m - 6)^2 \emph}$

$g)\\\\ 9x^2 + 12x + 4\\\\ ( 3x + 2) . ( 3x + 2) \\\\ \textbf{ ( 3x + 2)^2 \emph}$

$h)\\\\ 4m^2 - 20m + 25\\\\ ( 2m + 5) . ( 2m + 5) \\\\ \textbf{ ( 2m +5)^2 \emph}$

$i)\\\\ x^2 - 18x + 81\\\\ ( x - 9) . ( x - 9) \\\\ \textbf{ ( x + 9)^2 \emph}$

$j)\\\\ 16y^2 +8y + 1\\\\ ( 4y - 1) . ( 4y -1) \\\\ \textbf{ ( 4y - 1)^2 \emph}$

$k)\\\\ 9x^2 + 36x + 36\\\\ 9.(( x +2) . ( x + 2)) \\\\ \textbf{ 9 .( x + 2)^2 \emph}$

$l)\\\\ 25a^2 +60ab + 36b^2\\\\ ( 5a + 6b) . (5a + 6b) \\\\ \textbf{ ( 5a + 6b)^2 \emph}$

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