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Expand and simplify expressions

   

Added on  2023-04-20

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DIP1003 SEMESTER 1,2019
ASSIGNMENT 2
MARCH 26, 2019
Submitted by:
Timo Weiss
Expand and simplify expressions_1

1. Expand and simplify the following expressions:
a) (𝟒𝒙 + 𝒚)𝟐 − 𝟑𝒙(𝒚 + 𝟐𝒙)
Sol.
Using (𝑎 + 𝑏)2 = 𝑎2 + 𝑏2 + 2𝑎𝑏
(4𝑥 + 𝑦)2 − 3𝑥(𝑦 + 2𝑥)
= ((4𝑥)2 + 𝑦2 + 2(4𝑥)(𝑦)) − 3𝑥(𝑦 + 2𝑥)
= 16𝑥2 + 𝑦2 + 8𝑥𝑦 − 3𝑥𝑦 − 6𝑥2
= 10𝑥2 + 𝑦2 + 5𝑥𝑦
b)
(𝒙𝟒𝒚𝟎𝒛𝟔)
𝟏
𝟐(𝒙
−𝟑
𝟐 𝒚
𝟔
𝟐)
−𝟐
𝒙𝟒𝒚𝟐𝒛𝟑
𝒙−𝟒𝒚𝒛𝟑
Sol.
(𝑥4𝑦0𝑧6)1
2(𝑥−3
2 𝑦6
2)−2𝑥4𝑦2𝑧3
𝑥−4𝑦𝑧3
= (𝑥2𝑧3)𝑥4𝑦2𝑧3
(𝑥−3𝑦6)(𝑥−4𝑦𝑧3)
= 𝑥6𝑦2𝑧6
𝑥−7𝑦7𝑧3
= 𝑥13𝑦−5𝑧3
= 𝑥13𝑧3
𝑦5
2. Fid the values of x in the following equation using the rule that if 𝒂 ∗ 𝒃 = 𝟎 then 𝒂 =
𝟎 𝒐𝒓 𝒃 = 𝟎. Do not expand the equation or use the quadratic formula.
(𝟓𝒙 + 𝟔) (𝟑𝒙 − 𝟐
𝟑) = 𝟎
Sol.
𝐸𝑖𝑡ℎ𝑒𝑟 (5𝑥 + 6) = 0 𝑜𝑟 (3𝑥 − 2
3) = 0
5𝑥 + 6 = 0
𝑥 = −6
5
(3𝑥 − 2
3) = 0
Expand and simplify expressions_2

3𝑥 = 2
3
𝑥 = 2
9
𝑥 = −6
5 𝑜𝑟 2
9
3. Solve the following equation for 𝒎.
Hint: 𝒂𝟐 − 𝒃𝟐 = (𝒂 − 𝒃)(𝒂 + 𝒃)
(𝟐𝒎)𝟐 − 𝟒
𝒎𝟐 + 𝟏 = 𝟐𝒎 + 𝟐
𝒎 + 𝟐
Sol.
(2𝑚)2 − 4
𝑚2 + 1 = 2𝑚 + 2
𝑚 + 2
= (2𝑚)2 − 22
𝑚2 + 1 = 2𝑚 + 2
𝑚 + 2
= (2𝑚 + 2)(2𝑚 − 2)
𝑚2 + 1 = 2𝑚 + 2
𝑚 + 2
= 4(𝑚 + 1)(𝑚 − 1)
𝑚2 + 1 = 2(𝑚 + 1)
𝑚 + 2
= 2(𝑚 − 1)
𝑚2 + 1 = 1
𝑚 + 2
2(𝑚 − 1)(𝑚 + 2) = 𝑚2 + 1
2(𝑚2 + 2𝑚 − 𝑚 − 2) = 𝑚2 + 1
2𝑚2 + 𝑚 − 2 = 𝑚2 + 1
= 𝑚2 + 𝑚 − 3
4. Factorise the following expressions:
a) 𝟑𝟔𝒙𝟐 − 𝟖𝟏
Sol.
36𝑥2 − 81
= (6𝑥)2 − 92
𝑈𝑠𝑖𝑛𝑔 𝑎2 − 𝑏2 = (𝑎 + 𝑏)(𝑎 − 𝑏)
= (6𝑥 + 9)(6𝑥 − 9)
Expand and simplify expressions_3

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