Junior High School · Mathematics

Expansion and Factorization: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Expansion and Factorization.

10 questions27 marksFree, no account

Question 1

1 mark

次の式を展開しなさい。
\( (x + 7)(x - 7) \)

Question 2

1 mark

次の式を因数分解しなさい。
\( (x + 1)^2 - 4(x + 1) - 12 \)

Question 3

1 mark

次の式を因数分解しなさい。
\( (x - 2)^2 - 2(x - 2) - 15 \)

Question 4

1 mark

次の式を因数分解しなさい。
\( 5x^2 - 20 \)

Question 5

1 mark

次の式を因数分解しなさい。
\( 4a^2 - 20ab + 25b^2 \)

Question 6

2 marks

次の式を展開しなさい。
\( (x + 7)^2 \)

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

次の式を因数分解しなさい。
\( 2ax^2 - 12ax + 18a \)

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Question 8

5 marks

\( x^2 + 10x + a \) がある整式の2乗の形になるとき、定数 \( a \) の値を求めなさい。

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Question 9

4 marks

次の式を展開し、項を整理しなさい。
(1) \( (2x + 3y)^2 \)
(2) \( (a - 4b)(a + 4b) \)

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Question 10

7 marks

次の各問いに答えなさい。

(a) 式 \( (x^2 - 4x + 3)(x^2 - 4x - 5) + 12 \) を因数分解しなさい。

(b) \( x^2 - y^2 + 6y - 9 \) を因数分解しなさい。

(c) \( a, b \) を正の整数とする。方程式 \( a^2 - b^2 + 6b - 10 = 0 \) を満たす \( (a, b) \) の組をすべて求めなさい。

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