GRADE 10 Factorization
嚜澧AMI Mathematics
athematics:
athematics: Grade 10
10.4
GRADE 10_CAPS Curriculum
Algebraic expressions (B)
1. Factorization
1.1 Difference between two squares
(a)
(b)
(c)
(d)
(e)
c2 每 h2
25p2 每 9q2
81d8 每 16h12
64a10 每 256f4
(x - 1)2 - 36
1.2 Grouping
(a)
(b)
(c)
(d)
(d)
dj + hj + dq + hq
b2 每 b(e + r) + er
8b7 每 12b6e 每 4be6 + 6e7
a2 每 4h2 每 32hq 每 64q2
b2 每 b(f + z) + fz
1.3
Trinomials
(a) 3n2 每 11n 每 4
(b) 2g2 + g 每 1
(c) 2q2 每 15q + 28
(d) 25q2 每 20q 每 12
(e) -16k2 + 44k 每 24
(f) -28c 每 12c2 每 16
(g) 21b + 9b2 + 12
(h) -2k2q3 每 6kq3 每 4q3
(i) b2 每 9g2 每 48gz 每 64z2
(j) 49a2 + 56ag + 16g2 - 121q6
1.4 Sum or difference
difference between cubes
(a)
(b)
(c)
(d)
(e)
8a3 每 125c3
8p6 + 27r12
64n9 每 q9
2y3 每 16x3
256 每 32k9m6
1.5 Factorizing fractions
CAMI Mathematics
athematics:
athematics: Grade 10
(a)
e5
e9
‾
m4r 5 m2r 9
(b)
12m 2 + 132m m + 11
‾
12m
11
(c)
t 2 ? 9t t 2 ? 4t ? 45
‾
t 2 + 3t t 2 + 9t + 18
(d)
p 2 ? 64 9 p ? 72
‾
3p ? 9
3p
(e)
2mx 6 7 m 5 x 5
‾
m + x 8m + 8 x
(f)
36m 2 ? 8m
9m ? 2
CAMI Mathematics
athematics:
athematics: Grade 10
MEMO
1.1
Difference between two squares [4.5.3.1;
[4.5.3.1; 4.5.3.2; 4.5.3.3; 4.5.3.4; 4.5.3.5]
4.5.3.5]
(a)
c2 每 h2
= (c + h)(c - h)
(b)
25p2 每 9q2
= (5p + 3q)(5p 每 3q)
(c)
81d8 每 16h12
= (9d3 + 4h6) (9d3 - 4h6)
(d)
64a10 每 256f4
= (8a5 + 16f2) (8a5 - 16f2)
(e)
(x - 1)2 每 36
= ((x 每 1) + 6)((x 每 1) 每 6)
= (x + 5)(x - 7)
1.2 Grouping [4.5.2.1; 4.5.2.2; 4.5.2.3; 4.5.6.1]
4.5.6.1]
(a)
dj + hj + dq + hq
= (dj + hj) + (dq + hq)
= j(d + h) + q(d + h)
= (d + h)(j + q)
(b)
b2 每 b(e + r) + er
= b2 每 be 每 br + er
= (b2 每 be) + (-br + er)
= b(b 每 e) 每 r(b 每 e)
= (b 每 e)(b 每 r)
(c)
8b7 每 12b6e 每 4be6 + 6e7
= (8b7 每 12b6e) + (-4be6 + 6e7)
= 4b6(2b 每 3e) 每 2e6(2b 每 3e)
= (2b 每 3e)(4b6 每 2e6)
= 2(2b 每 3e)(2b6 每 e6)
(d)
a2 每 4h2 每 32hq 每 64q2
= a2 每 4(h2 + 8hq + 16q2)
= a2 每 4(h + 4q)2
CAMI Mathematics
athematics:
athematics: Grade 10
= (a + 2(h + 4q))(a 每 2(h + 4q))
= (a + 2h + 8q)(a 每 2h 每 8q)
(d)
b2 每 b(f + z) + fz
= b2 每 bf 每 bz + fz
= (b2 每 bf) + (每 bz + fz)
= b(b 每 f) 每 z(b 每 z)
= (b 每 f)(b 每 z)
1.3
Trinomials [4.5.4.2; 4.5.4.3; 4.5.5.2; 4.5.5.3]
4.5.5.3]
(a)
3n2 每 11n 每 4
= (3n + 1)(n 每 4)
(b)
2g2 + g 每 1
= (g + 1)(2g 每 1)
(c)
2q2 每 15q + 28
= (2q 每 7)(q 每 4)
(d)
25q2 每 20q 每 12
= (5q 每 6)(5q + 2)
(e)
-16k2 + 44k 每 24
= -4(4k2 每 11k + 6)
= -4(4k 每 3)(k 每 2)
(f)
-28c 每 12c2 每 16
= -4(7c + 3c2 + 4)
= -4(3c2 + 7c + 4)
= -4(3c + 4)(c + 1)
(g)
21b + 9b2 + 12
= 3(7b + 3b2 + 4)
= 3(3b2 + 7b + 4)
= 3(3b + 4)(b + 1)
(h)
-2k2q3 每 6kq3 每 4q3
= -2q3(k2 + 3k + 2)
= -2q3(k + 2)(k + 1)
(i)
b2 每 9g2 每 48gz 每 64z2
= b2 每 (9g2 + 48gz + 64z2)
CAMI Mathematics
athematics:
athematics: Grade 10
= b2 每 (3g + 8z)2
= (b + (3g + 8z))(b 每 (3g + 8z))
= (b + 3g + 8z)(b 每 3g 每 8z)
(j)
49a2 + 56ag + 16g2 - 121q6
= (7a + 4g)2 每 121q6
= (7a + 4g + 11q3)(7a + 4g 每 11q3)
1.4 Sum or difference between cubes [4.5.8
[4.5.8]
4.5.8]
(a)
8a3 每 125c3
=(2a 每 5c)(4a2 + 10ac + 25c2)
(b)
8p6 + 27r12
= (2p3 + 3r4)(4p6 每 6p3r4 + 9r8)
(c)
64n9 每 q9
= (4n3 - q3)(16n6 + 4n3q3 + q6)
(d)
2y3 每 16x3
= 2(y3 每 8x3)
= 2(y 每 2x)(y2 + 2xy + 4x2)
(e)
256 每 32k9m6
= 32(8 每 k9m6)
= 32(8 每 k3m6)
= 32(2 每 km2)(4 + 2km2 + k2m4)
1.5 Factorizing fractions [4.8.5.1; 4.8.5.2; 4.8.5.3; 4.8.5.4; 4.8.7.3; 4.8.7.1]
4.8.7.1]
(a)
e5
e9
‾
m4r 5 m2r 9
e5
m2r 9
= 4 5℅ 9
mr
e
4
r
= 2 4
me
(b)
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