ExeUSET
1. a) 343x + 8y3 + 294x+y + 84xy2
b) -27x + 512y2 + 144x+y - 384xy2
c) 125a + 64b3 + 300a²b + 240ab2
d) 27p2 – 892-54p q + 36pg?
e) x6 - 8y3 - 6x4y + 12x2y2
f) x3/8 + 13 + 3/4x+y + 3/2xy?
g) a3/27 - 03/125 - (ab)/15 + (ab)/25
h) pq? - 8r3 - 6p?q?r + 12pqr?
2. a) (4x + 2y) – 24xy(4x + y)
b) (-2a + 3b) + 18ab(-2a + 3b)
c) (3x - 5y) + 45xy(3x - 5y)
d) (x2/2 - 3y)3 + 9/2x2y(x2/2 - 3y)
3. a) x2 + 4y2 + 9z2 + 4xy + 12yz + 6xz
b) a2 +962 +42-6ab- 12bc + 4ca
c) 4p2 +257 + 12 + 20pq - 10qr - 4rp
d) x2 + 25y2 + 92 - 10xy + 20yz - 6xz
e) a2 + 2562 + 160 + 10ab + 40bc + Sca
f) p2 + 4q2 + 16r3 - 4pq - 16gr + Srp
4. a) 250x + 270xy
b) 263 +216a_b
c) 16p3 + 12pg?
d) -54n - 18mn
5. a) 95
b) 2240 c) 90 d) 1000
6. a) 994011992
b) 1012048064
c) 912673
d) 1030301
Answers
Answer:
these work before moving on:
(a) 3a + 12b – 5a + 7b – 2a = – 4a + 19b
(b) x² + 5x – 5 + 4x² – 3x + 5 = 5x² + 2x (these two terms can not be added as one is x and the other is x²)
(c) 2p + 3pq – 5pq² + 6p – pq = 8p + 2pq – 5pq²
Practice Questions
Work out the answer to each question then click on the button marked to see if you are correct.
Simplify these expressions by collecting like terms:
(a) 3p + 6q – 5p + 3q
(b) x3 – 4x2 + 7x – 3 + 7x2 – 9x + 1
(c) ab2 + 3ab - 3a + 2ab2 - 5ba + 4a
Laws of Indices
Rules to learn
positive powers an means multiply together n lots of a
e.g. a5 = a × a × a × a × a
multiplying powers If the bases are the same then you add the powers: am × an = a(m + n)
e.g. x5 × x3 = x8
dividing powers If the bases are the same then you subtract the powers: am ÷ an = a(m – n)
e.g. y2 ÷ y6 = y– 4
This also works for powers in fractions: e.g. p7 = p3 p4
powers of powers The powers are multiplied: (am)n = a(mn)
e.g. (z2)5 = z10
special powers a1 = a and a0 = 1
e.g. b4 ÷ b3 = b1 = b
e.g. d 3 × d – 3 = d 0 = 1
multiplying terms To multiply terms, multiply the coefficients to get the new coefficient then multiply each letter in turn:
e.g. 3x2 × 5x3 = 15x5
e.g. 4xy 2 × x3 × 3x
Answer:
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