Class 8 Multiplying Polynomials — practice questions with answers

Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Multiply:

4 x \times 3 y

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Answer: B)

12 x y

Multiply the numbers and then the variables:

4 \times 3 = 12

x \times y = x y

. So

12 x y

. Coefficients are multiplied, not added.

2. Find

(x + 3) (x + 5)

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Answer: A)

x^{2} + 8 x + 15

x \cdot x + 5 x + 3 x + 15 = x^{2} + 8 x + 15

. Dropping the middle terms gives the wrong

x^{2} + 15

3. Expand

(3 m - 2 n) (2 m - 5 n)

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Answer: B)

6 m^{2} - 19 mn + 10 n^{2}

6 m^{2} - 15 mn - 4 mn + 10 n^{2} = 6 m^{2} - 19 mn + 10 n^{2}

(- 2 n) (- 5 n) = + 10 n^{2}

4. Simplify

2 x (3 x - y) - 3 y (x - 2 y)

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Answer: A)

6 x^{2} - 5 x y + 6 y^{2}

6 x^{2} - 2 x y - 3 x y + 6 y^{2} = 6 x^{2} - 5 x y + 6 y^{2}

- 3 y \times (- 2 y) = + 6 y^{2}

5. Simplify

(3 x + 2 y) (x - y) + (x + y) (x - 2 y)

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Answer: B)

4 x^{2} - 2 x y - 4 y^{2}

First:

3 x^{2} - x y - 2 y^{2}

. Second:

x^{2} - x y - 2 y^{2}

. Sum:

4 x^{2} - 2 x y - 4 y^{2}

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