Question

find the coefficient of x² in the expression of ( x²+x+1)²+(x²-x+1)²
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Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

Find the coefficient of x² in (x²+x+1)²+(x²-x+1)²

♣ ɢɪᴠᴇɴ :

(x²+x+1)²+(x²-x+1)²

♣ ᴛᴏ ꜰɪɴᴅ :

Coefficient of x²

♣ ᴀɴꜱᴡᴇʀ :

In ( x²+x+1)²+(x²-x+1)², coeffiecient of x² = 2

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

(x²+x+1)²+(x²-x+1)²

= (x²+x+1)²+(x²-x+1)²

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Using algebraic identity : (a+b+c)² = a² + b² + c² + 2(ab + bc + ca)

(x²+x+1)² = x⁴ + x² + 1 + 2(x²x + 1x +1x²)

Using algebraic identity : (a-b+c)² =a² + b² + c² - 2(ab + bc -ac)

(x²-x+1)² = x⁴ + x² + 1 - 2(x²x + 1x - 1x²)

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(x²+x+1)²+(x²-x+1)²

= x⁴ + x² + 1 + 2(x²x + 1x + 1x²) + x⁴ + x² + 1 - 2(x²x + 1x - 1x²)

= x⁴ + x² + 1 + 2x²x + 2x + 2x² + x⁴ + x² + 1 - 2x²x + 2x - 2x²

= 2x⁴ + 2x² +2

A coefficient is a number multiplied by a variable.

In ( x²+x+1)²+(x²-x+1)², coeffiecient of x² :

= 2