Factorise :- (x²-1)²+8x(x²+1)+19x²
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Answered by
24
Answer:
(x² + 3x + 1)(x² + 5x + 1)
Step-by-step explanation:
Given Equation is (x² - 1)² + 8x(x² + 1) + 19x²
⇒ x⁴ + 1 - 2x² + 8x³ + 8x + 19x²
⇒ x⁴ + 8x³ + 17x² + 8x + 1
⇒ x⁴ + 5x³ + 3x³ + 15x² + 2x² + 5x + 3x + 1
⇒ x⁴ + 5x³ + 3x³ + 15x² + x² + x² + 5x + 3x + 1
On rearranging the terms,we get
⇒ x⁴ + 5x³ + x² + 3x³ + 15x² + 3x + x² + 5x + 1
⇒ x²(x² + 5x + 1) + 3x(x² + 5x + 1) + 1(x² + 5x + 1)
⇒ (x² + 3x + 1)(x² + 5x + 1)
Hope it helps!
mathematics15262:
Thank u very nucbe
Much
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Very very thank u
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One more question am adding
any doubts ask in inbox..other users will be disturbed here!
Yes
Answered by
15
Step-by-step explanation:
(x² - 1)² + 8x(x² + 1) + 19x²
x⁴ + 1 - 2x² + 8x³ + 8x + 19x²
x⁴ + 8x³ + 17x² + 8x + 1
x⁴ + 5x³ + 3x³ + 15x² + 2x² + 5x + 3x + 1
x⁴ + 5x³ + 3x³ + 15x² + x² + x² + 5x + 3x + 1
x⁴ + 5x³ + x² + 3x³ + 15x² + 3x + x² + 5x + 1
x²(x² + 5x + 1) + 3x(x² + 5x + 1) + 1(x² + 5x + 1)
(x² + 3x + 1)(x² + 5x + 1)
Nice steps
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