Grade 7 Polynomial Questions: Add and Subtract with Step-by-Step Solutions

Adding, subtracting and simplifying polynomials are an important skills in algebra and maths in general. Grade 7 maths multiple choice questions on adding and subtracting polynomials with answers are presented in this page.

To add polynomials in algebra, we group like terms and simplify.

Example 1: Simplifying Linear Expressions

1. Given: \( (2x + 5) + (4x + 6) \)
2. Group like terms inside parentheses: \( = (2x + 4x) + (5 + 6) \)
3. Simplify: \( = 6x + 11 \)

Example 2: Simplifying Quadratic Expressions

1. Given: \( (x^{2} - 6x - 9) + (-5x^{2} + 9x + 2) \)
2. Group like terms inside parentheses:\( = (x^{2} - 5x^{2}) + (-6x + 9x) + (-9 + 2) \)
3. Simplify \( = -4x^{2} + 3x - 7 \)

Example 3: Subtraction of two Polynomials

When subtracting a second polynomial from a first polynomial, follow these steps:

• First, place the polynomials in parentheses.
• Change the subtraction sign into addition.
• Change the sign of every term in the second polynomial.
• Group like terms (terms with the same variables and exponents).
• Simplify by combining the like terms.

1. Given: \( (2xy + x + 5) - (3xy - 2x + 7) \)
2. Change the subtraction into addition and change signs of the terms in polynomial: \( = (2xy + x + 5) + (-3xy + 2x - 7) \)
3. Group like terms inside parentheses: \( = (2xy - 3xy) + (x + 2x) + (5 - 7) \)
4. Simplify: \( = -xy + 3x - 2 \)

Multiple Choice Questions

1. Add the polynomials: \( (9x - 6) + (-5x + 7) \)
   
   1. \(14x + 1\)
   2. \(-4x - 1\)
   3. \(4x + 1\)
   4. \(4x + 13\)
2. Subtract the polynomials: \( (9x - 6) - (-5x + 7) \)
   1. \(14x - 13\)
   2. \(4x + 1\)
   3. \(-4x + 13\)
   4. \(-4x - 13\)
3. Add the polynomials: \( (-x^{2} + 5x + 2) + (6x^{2} + x) \)
   1. \(7x^{2} + 6x + 2\)
   2. \(5x^{2} + 6x + 2\)
   3. \(5x^{2} + 6x\)
   4. \(7x^{2} + 6x\)
4. Subtract the polynomials: \( (-x^{2} + 5x) - (6x^{2} + x - 2) \)
   1. \(-5x^{2} + 6x + 2\)
   2. \(5x^{2} + 6x - 2\)
   3. \(5x^{2} + 6x\)
   4. \(-7x^{2} + 4x + 2\)
5. Add the polynomials: \( (-7x^{2}y + xy + 3x + 2) + (5x^{2}y - 5xy - 6x - 7) \)
   
   1. \(-2x^{2}y - 4xy - 3x - 5\)
   2. \(2x^{2}y + 4xy - 3x - 5\)
   3. \(-2x^{2}y - 4xy + 3x + 5\)
   4. \(2x^{2}y + 4xy + 3x + 5\)
6. Subtract the polynomials: \( (-7x^{2}y + xy + 3x + 2) - (5x^{2}y - 5xy - 6x - 7) \)
   1. \(-2x^{2}y - 4xy - 2x - 5\)
   2. \(-12x^{2}y + 6xy + 9x + 9\)
   3. \(-12x^{2}y - 6xy - 9x - 9\)
   4. \(12x^{2}y + 6xy + 9x + 9\)
7. Add the polynomials: \( (xy + 3x + 2) + (3x^{2} + y) \)
   1. \(3x^{2} + 4xy + 2\)
   2. \(3x^{2} + 2xy + 3x + 2\)
   3. \(3x^{2} + xy + 3x + y + 2\)
   4. \(3x^{2} + 5xy + 2\)
8. Subtract the polynomials: \( (xy + 3x + 2) - (3x^{2} + y) \)
   1. \(3x^{2} + 4xy + 2\)
   2. \(3x^{2} + 4xy + 2\)
   3. \(-3x^{2} + 3x - y + 2\)
   4. \(-3x^{2} + xy + 3x - y + 2\)
9. Add the polynomials: \( (x^{2}y + 3x + 2) + (2 + 2xy^{2} + 3x) \)
   1. \(x^{2}y + 2xy^{2} + 6x + 4\)
   2. \(3x^{2}y + 6x + 4\)
   3. \(3xy^{2} + 6x + 4\)
   4. \(3x^{2}y^{2} + 6x + 4\)
10. Subtract the polynomials: \( (x^{2}y + 3x + 2) - (2 + xy^{2} + 3x) \)
    1. \(0\)
    2. \(-2x^{2}y\)
    3. \(x^{2}y - xy^{2}\)
    4. \(x^{2}y + xy^{2}\)

Answers to the Above Questions

1. C
2. A
3. B
4. D
5. A
   
6. B
7. C
8. D
9. A
10. C

Links and References

• Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
• High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
• Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
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