32031中３・多項式の因数分解・計算問題・因数分解の公式2-1

2023年3月25日 2023年7月7日

banno

次の式を展開しなさい。

(1) $x^{2} + 2 x + 1$

(2) $x^{2} + 8 x + 16$

(3) $x^{2} + 12 x + 36$

(4) $x^{2} - 4 x + 4$

(5) $x^{2} - 16 x + 64$

(6) $x^{2} - 20 x + 100$

解答・解説

公式２ $x^{2} + 2 a x + a^{2} = (x + a)^{2}$

公式３ $x^{2} - 2 a x + a^{2} = (x - a)^{2}$

(1) $\begin{array}{r} x^{2} + 2 x + 1 \end{array}$

$\begin{array}{rcl} = & x^{2} + 2 \times 1 \times x + 1^{2} \\ = & (x + 1)^{2} \end{array}$

答 $(x + 1)^{2}$

(2) $\begin{array}{r} x^{2} + 8 x + 16 \end{array}$

$\begin{array}{rcl} = & x^{2} + 2 \times 4 \times x + 4^{2} \\ = & (x + 4)^{2} \end{array}$

答 $(x + 4)^{2}$

(3) $\begin{array}{r} x^{2} + 12 x + 36 \end{array}$

$\begin{array}{rcl} = & x^{2} + 2 \times 6 \times x + 6^{2} \\ = & (x + 6)^{2} \end{array}$

答 $(x + 6)^{2}$

(4) $\begin{array}{r} x^{2} - 4 x + 4 \end{array}$

$\begin{array}{rcl} = & x^{2} - 2 \times 2 \times x + 2^{2} \\ = & (x - 2)^{2} \end{array}$

答 $(x - 2)^{2}$

(5) $\begin{array}{r} x^{2} - 16 x + 64 \end{array}$

$\begin{array}{rcl} = & x^{2} - 2 \times 8 \times x + 8^{2} \\ = & (x - 8)^{2} \end{array}$

答 $(x - 8)^{2}$

(6) $\begin{array}{r} x^{2} - 20 x + 100 \end{array}$

$\begin{array}{rcl} = & x^{2} - 2 \times 10 \times x + 10^{2} \\ = & (x - 10)^{2} \end{array}$

答 $(x - 10)^{2}$