Algebraic Expressions [1 marks]
1. Expand (a + y)2.
2. Expand (3x + y)2.
3. Express a2 – b2 in terms of factors.
4. Express x3-y3 in terms of factors.
5. Factorize x2 – xy + x – y.
6. Factorize p2 – 15q – 5p + 3pq.
7. Factorize 2a2 + 3pa +2pa + 3p2.
8. Find the factors of 2pq + 3 + 6p + q.
9. Find the factors of a2 – 12b2 – 2ab + 6ab.
10. Find the factors of ab + bc + ax + cx.
Answers:
1. a2 + 2ay + y2
2. 9x2 + 6xy + y2
3. (a – b) (a + b)
4. (x – y) (x2 + xy +y2)
5. (x – y) (x + 1)
6. (p – 5) (p + 3q)
7. (a + p) (2a + 3p)
8. (2p + 1) (q + 3)
9. (a + 2b) (a – 6b)
10. (b + x) (a + c)
Algebraic Expressions [2 marks]
1. Factorize a2 – 10a + 24.
2. Factorize x2 + 14x + 49.
3. Factorize p2 – 8p + 16.
4. Factorize a2 – 26a + 169.
5. Factorize 9x2 – y2 -6y – 9.
6. Find the value of
![\[ a^{2}+ \frac{1}{{a}^{2}} if a^{2}+ \frac{1}{{a}}=7 \]](https://swoadhyan.com/wp-content/ql-cache/quicklatex.com-8115c4804a56329360dc369dcdf6cdff_l3.png "Rendered by QuickLaTeX.com")
7. Illustrate (a + b)2 = a2 + 2ab + b2 using blocks. [ use figures]
8. Illustrate x2 – x – 12 in a diagram.
9. Find the value of a3 + b3 if a + b = 5 and ab = 10.
10. Find the value of (a + b)3 – (a – b)3 if a = 3 and b = 1.
Answers:
1. (a – 6) (a – 4)
2. (x + 7) (x + 7)
3. (p – 4) (p – 4)
4. (a – 13) (a – 13)
5. 3(x + y) (x – 2)
6. 47
9. -25
10. 56
