Chapter 13 Volume of prisms

Chapter 15 Working with variables
Activity 15.1
1. (x – 5)²
= (x – 5)(x – 5)
= x² – 5x – 5x + 25
= x² – 10x + 25
2. They are both 5x.
3. Find the product of the two terms in the expression,
and double the product.
Exercise 15.1
1. (a) 3y + 18 (b) 4r² – 4r
(c) 6e + 6f
(d) 3a² + 3ab
(e) m²n – mn² (f) 2u² – 2uv
(g) 16k – 8jk
(h) 4pr² + 28p²r
(i) 30i + 6i²
(j) 8yk + 8y + 8yx
2. (a) 10a + 4 (b) 4tr + 42t + 2r
(c) 7m² + 2m
(d) 8u² – 13u
(e) 2rs + 4rt + 4ru (f) 12y² – 3y – 12
(g) 3b² + 26ab – 10a² (h) –3e² + 13e – 28
(i) –3t² + 5t (j) 4xm²n – 14x²
3. (a) 6r (b) 24t (c) –12ab (d) –24yz
4. (a) a² + 2a + 1 (b) b² + 6b + 9
(c) x² + 2xy + y² (d) 9d² + 12de + 4e²
(e) f² – 12f + 36 (f) g² – 2gh + h²
(g) 9d² – 12de + 4e² (h) 49p² –28pq + 4q²
(i) 25t² + 60t + 36 (j) 144r² + 72rs + 9s²
5. 49p 4 + 14p²q + q²
6. (a) (7x + 3)² (Any variable can be used.)
(b) 49x² + 42x + 9
7. (a) x² + 2x + 1 (b) y² – 6y + 9
(c) 4x² + 12x + 9 (d) 16x² + 8xy + y²
(e) 9x² + 18xy + 9y² (f) 64x² – 32xy + 4y²
(g) 16y² – 8xy + x²
(h) 121x² + 264xy + 144y²
(i) 64x² + 112xy + 49y² (j) 25y² + 90xy + 81x²
8. She has not doubled the product of the two terms,
to get the middle term. She has also forgotten to
square the 9 in the first term.
9. Correct. Since the binomial is being squared, the
first and last terms are also squared. Squaring a
positive or a negative number results in a positive
number.
10. (2x – 3y)² = 4x² – 12xy + 9y²
Exercise 15.2
1. (a) 6 (b) 2x (c) m (d) x
(e) 9w (f) 16ac (g) 4uv (h) 3m
2. P = 2(l + w)
3. (a) 12m(m – 2) (b) 4vr(1 + 2v)
(c) 2ab(5a + b) (d) 3g(2h²g – 6h + 1)
(e) 88xyz + 77xy² = 11xy(8z + 7y)
4. (a) b(4b + 1) (b) a(12 + 3b – 4c)
(c) t²(5 + 6r)
(d) 5(x² – 2y²)
(e) 3(6xy – 3x + y) (f) 2r(r + 1 + s)
(g) 3ab(4a + b) (h) 2y(z + 4)
(i) 5y(1 – 5y) (j) q(12 + 8r + q)
5. (a) (y + 1)(7 – a) (b) (r² – 1)(4 + t)
(c) (x – ½)(5 + w) (d) (m + n)(9 – i)
(e) (x – 4)(3x + 7)
(f) (b – 1)(4a + 2a²) = (b – 1)2a(2 + a)
6. (a) 18yp(4y – p)
(b) 3(x² – x + 3y – 4)
(c) 5a(4b² + b – 2a + 3ab)
(d) 2i(–6h + h² – 8i)
(e) 6a(b + 2bc – 3a)
(f) (h – 1)(g² + t + r²)
(g) 11efg(2e – fg + 11 – 9g)
(h) 27y²(3 – 4x)
(i) 15(3utv + ut² – 2u²v² + 4tv²)
(j) 6st(6s – 3 + 2st + 8t)
Extension activity
1. 2b(2a + b) 2. 3xy(1 – 3x)
3. r(12r – 4t + 3t²) 4. 5(2x + y)
5. 11hf(g + 4h) 6. 20pq(5p – 4q)
7. ab(2 – 2b + a) 8. –2i(4i + 9j)
9. 3r(1 + 2r – 4m) 10. uvw(17 + 4uvw)
Activity 15.2
1. (y + 2)(x + 1) 2. (b + 1)(x + 1)
3. (x – y)(m + 3) 4. (y – 2)(a + 3)
Exercise 15.3
1. (a) 10 (b) –28 (c) 18 (d) 36
(e) –8 (f) 16 (g) 30 (h) 4
2. (a) 7 (b) –4 (c) 40 (d) 1
(e) 66 (f) 28
3. 460 m 4. 40.5 kg
5. (a) 8a + 12b + 3c
(b) P6.40 + P13.20 + P8.70 = P28.30
6. (a) 156 (b) 2 022 (c) 1 017
(d) –32 (e) –112
7. (a) (x + x + 2 + 2x – 1) cm
= (4x + 1) cm
(b) 73 cm
8. P33.20 9. 720
10. (a) 5a + 3 where a is Sewela’s age.
(b) 63 years old
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