factorise this : 49 x to the power 4 - 168 x to the power 2 into Y to the power 2 + 144 Y to the power 4
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Answer:
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factorize49x^4-168x^2y^2+144y^4
49x4-168x2y2+144y4
Final result :
(7x2 - 12y2)2
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((49•(x4))-((168•(x2))•(y2)))+(24•32y4)
Step 2 :
Equation at the end of step 2 :
((49 • (x4)) - ((23•3•7x2) • y2)) + (24•32y4)
Step 3 :
Equation at the end of step 3 :
(72x4 - (23•3•7x2y2)) + (24•32y4)
Step 4 :
Trying to factor a multi variable polynomial :
4.1 Factoring 49x4 - 168x2y2 + 144y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (7x2 - 12y2)•(7x2 - 12y2)
Detecting a perfect square :
4.2 49x4 -168x2y2 +144y4 is a perfect square
It factors into (7x2-12y2)•(7x2-12y2)
which is another way of writing (7x2-12y2)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Trying to factor as a Difference of Squares :
4.3 Factoring: 7x2-12y2
Put the exponent aside, try to factor 7x2-12y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 7 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
(7x2 - 12y2)2
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Identifying Perfect Squares
Factoring Multi Variable Polynomials
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