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Question
Use the formula to expand:
(2) (4x + y – 7)2
(2) (4x + y – 7)2
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Solution
We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.
Comparing (4x + y – 7)2 with (a + b + c)2 , we get:
a = 4x, b = y and c = –7
Substituting these in the above formula:
(4x + y – 7)2 = (4x)2 + y2 + (–7)2 + 2 × 4x × y + 2 × y × (–7) + 2 × (–7) × 4x
= 16x2 + y2 + 49 + 8xy – 14y – 56x
Comparing (4x + y – 7)2 with (a + b + c)2 , we get:
a = 4x, b = y and c = –7
Substituting these in the above formula:
(4x + y – 7)2 = (4x)2 + y2 + (–7)2 + 2 × 4x × y + 2 × y × (–7) + 2 × (–7) × 4x
= 16x2 + y2 + 49 + 8xy – 14y – 56x
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