Calvin Wong Tuition's answer to Gabriel's Secondary 4 A Maths Singapore question.
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From Calvin W
Date Posted:
4 years ago
omg I sub in wrong place thanks
It's ok
Even the third and fourth lines need to have "+...".
It is likely that 1 mark will be deducted from the working for this inaccuracy, since truncating the expansion without "+..." means that the expansion of the terms stops there.
It is likely that 1 mark will be deducted from the working for this inaccuracy, since truncating the expansion without "+..." means that the expansion of the terms stops there.
Not just the 3rd and 4th line, it's every line. Notice that the (1 - 4x)³ was not fully expanded and there was no '+ ...'
Also there's a slight error in that it's 64a²x² , missing the exponent there
(1 + ax)⁴ (1 - 4x)³
= (1 + 4ax + 6(ax)² + ...)(1 + 3(-4x) + 3(-4x)² +...)
= (1 + 4ax + 6a²x² +...)(1 - 12x + 48x² +...)
= 1 - 12x + 48x² + 4ax - 48ax² + 6a²x² +...
= 1 + (4a - 12)x + (48 - 48a + 6a²)x² +...
(You may also use the ≈ sign if you don't want to write the +...)
Since the first 2 terms are p and qx²,
p = 1
4a - 12 = 0
4a = 12
a = 3
q = 48 - 48(3) + 6(3²)
= 48 - 144 + 54
= -42
= (1 + 4ax + 6(ax)² + ...)(1 + 3(-4x) + 3(-4x)² +...)
= (1 + 4ax + 6a²x² +...)(1 - 12x + 48x² +...)
= 1 - 12x + 48x² + 4ax - 48ax² + 6a²x² +...
= 1 + (4a - 12)x + (48 - 48a + 6a²)x² +...
(You may also use the ≈ sign if you don't want to write the +...)
Since the first 2 terms are p and qx²,
p = 1
4a - 12 = 0
4a = 12
a = 3
q = 48 - 48(3) + 6(3²)
= 48 - 144 + 54
= -42
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