Simplify the following algebraic expressions :
1) 4a + 2b + a
2) x2 + 3x + 2x + 5x2
3) 4a3 + 6a + 3a3 + 8a
4) 6x + 2(2x + 7)
5) 5n + 4(3n + 9)
6) 3(x + 2y) + 4(3x + y)
7) 3.2(x + y) + 2.3(x + y) + 4x
8) 3(4m + n) + 2m
9) 6(0.4f + 0.2g) + 0.5f
10) 3/4 + [(2/3) (s + 2t)] + s
11) (2/3)(y2 - y - 3) + (1/3)(y2 + 2y + 6)
12) 3[6a - 3(1 - a) - 5(a + 1)]
1. Answer :
= 4a + 2b + a
= 4a + a + 2b
= 5a + 2b
2. Answer :
= x2 + 3x + 2x + 5x2
= x2 + 5x2 + 3x + 2x
= 6x2 + 5x
3. Answer :
= 4a3 + 6a + 3a3 + 8a
= 4a3 + 3a3 + 6a + 8a
= 7a3 + 14a
4. Answer :
= 6x + 2(2x) + 2(7)
= 6x + 4x + 14
= 10x + 14
5. Answer :
= 5n + 4(3n) + 4(9)
= 5n + 12n + 36
= 15n + 36
6. Answer :
= 3(x + 2y) + 4(3x + y)
= 3(x) + 3(2y) + 4(3x) + 4(y)
= 3x + 6y + 12x + 4y
= 3x + 12x + 6y + 4y
= 15x + 10y
7. Answer :
= 3.2(x + y) + 2.3(x + y) + 4x
= 3.2(x) + 3.2(y) + 2.3(x) + 2.3 (y) + 4x
= 3.2 x + 3.2y + 2.3x + 2.3 y + 4x
= 3.2x + 2.3x + 4x + 3.2y + 2.3y
= 9.5x + 5.5y
8. Answer :
= 3(4m + n) + 2m
= 3(4m) + 3(n) + 2m
= 12m + 3n + 2m
= 14m + 3n
9. Answer :
= 6(0.4f + 0.2g) + 0.5f
= 6(0.4f) + 6(0.2g) + 0.5f
= 2.4f + 1.2g + 0.5f
= 2.4f + 0.5f + 1.2g
= 2.9f + 1.2g
10. Answer :
= 3/4 + [(2/3)(s + 2t)] + s
= 3/4 + [(2/3)(s) + (2/3)(2t)] + s
= 3/4 + 2s/3 + 4t/3 + s
= 3/4 + 2s/3 + s + 4t/3
= 3/4 + 2s/3 + 3s/3 + 4t/3
= 3/4 + (2s + 3s)/3 + 4t/3
= 3/4 + 5s/3 + 4t/3
11. Answer :
= (2/3)(y2 - y - 3) + (1/3)(y2 + 2y + 6)
= 2y2/3 - 2y/3 - 6/3 + y2/3 + 2y/3 + 6/3
= 2y2/3 + y2/3 - 2y/3 + 2y/3 - 6/3 + 6/3
= (2y2 + y2)/3
= 3y2/3
= y2
12. Answer :
= 3[6a - 3(1 - a) - 5(a + 1)]
= 3[6a - 3 + 3a - 5a - 5]
= 3[4a - 8]
= 12a - 24
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