### Chap 5 Algebra: 6 A.M. QUIZ (23 May 2010) (I)

Simplify (with complete working)

a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)

Note: This is a 2-mark question.

1. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
= (aa + ax) - (bc + bx) - (ca + cx) + (ac - ax) +
(cb + cx)
= aa - bc - bx - ca - cx + ac + cb + cx
= aa - bx - ca - cx + ac + cx
= aa - bx - ca + ac
= aa - bx

2. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
= (aa + ax) - (bc + bx) - (ca + cx) + (ac - ax) + (cb + cx)
= aa + ax - bc - bx - ca - cx + ac - ax + cb +cx
= aa + (ax - ax) + (bc - cb) + (ac - ca) + (cx - cx) - bx
= aa + 0 + 0 + 0 + 0 - bx
= aa - bx

JJ(:

3. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
= (aa + ax) - (bc + bx) - (ca + cx) + (ac - ax) +
(cb + cx)
= aa - bc - bx - ca - cx + ac + cb + cx
= aa - bx - ca - cx + ac + cx
= aa - bx - ca + ac
= aa - bx

4. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
= (aa + ax) - (bc + bx) - (ca + cx) + (ac - ax) +
(cb + cx)
= aa - bc - bx - ca - cx + ac + cb + cx
= aa - bx - ca - cx + ac + cx
= aa - bx - ca + ac
= aa - bx

5. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
= (a x a + a x x)- (b x c + b x x) - (c x a + c x x) + (a x c - x x a) + (c x b + x x c)
= aa + ax - bc + bx - ca + cx + ac - ax + cb + cx
=aa+ ( ax - ax) + (-bc + bc) - bx - (ca + ac) +(-cx+cx)
=aa - bx

6. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
=a^2+ax - bc- bx - ca - cx + ac - ax + cb +cx
=a^2+ax-ax-bc+cb-ca+ac-cx+cx-bx
=a^2-bc+cb-ca+ac-cx+cx-bx
=a^2-ca+ac-cx+cx-bx
=a^2-cx+cx-bx
=a^2-bx

7. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
=a^2 +ax -bc -bx -ac -cx +ac -cx +ac -ax +bc +cx
=a^2 +ax -ax -bc +bc -bx -ac +ac -cx +cx
=a^2 -bx

8. a(a + x) - b(c + x) - c(a + x) + a(c - x) + c(b + x)
=(aa+ax)-(bc+bx)-(ca+cx)+(ac-ax)+(cb+cx)
=aa+ax-bc-bx-ca-cx+ac-ax+cb+cx
=aa-bx

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