2. If 3x + 2y = 12 and xy = 6, find the value of 9x2 + 4y2.
3. Write the following cubes in the expanded form:
(i) (3a + 4b)3
(ii) (5p – 3q)3
4. If  find the values of each of the following:
(i) 
(ii) 
5. If  then evaluate 
6. If a + b + c = 15 and a2 + b2 + c2 = 83, find the value of a3 + b3 + c3 – 3abc.
7. Factorize:
(i) 6ab – b2 + 12ac – 2bc
(ii) 9(2a – b)2 – 4(2a – b) – 13
8. If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2, find the values of a and b.
9. Using factor theorem, factorize each of the following polynomials:
(i) x3 – 6x2 + 3x + 10
(ii) 2y3 – 5y2 – 19y + 42
Answers
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Answer:
3x+2y=12
Squaring both sides, we get
(3x+2y)
2
=144
⇒9x
2
+4y
2
+2×3x×2y=144
⇒9x
2
+4y
2
=144−12xy
⇒9x
2
+4y
2
=144−12×6 since xy=6
⇒9x
2
+4y
2
=144−72=72
∴9x
2
+4y
2
=72
2 The given statement is:]
(3a+4b)^3(3a+4b)
3
Using the identity (a+b)^3=a^3+b^3+3a^2b+3ab^2(a+b)
3
=a
3
+b
3
+3a
2
b+3ab
2
, we have
=(3a)^3+(4b)^3+3(3a)^2(4b)+3(3a)(4b)^2(3a)
3
+(4b)
3
+3(3a)
2
(4b)+3(3a)(4b)
2
=27a^3+64b^3+108a^2b+144ab^227a
3
+64b
3
+108a
2
b+144ab
2
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