Factorise the equation :- -9x^2 + 24xy - 16y^2
Answers
Answer:
3 • (x - 4y)2
Step-by-step explanation:
STEP1: Equation at the end of step 1
((3 • (x2)) - 24xy) + (24•3y2)
((3 • (x2)) - 24xy) + (24•3y2)
STEP 2 : Equation at the end of step2:
(3x2 - 24xy) + (24•3y2)
(3x2 - 24xy) + (24•3y2)
STEP3: Pulling out like terms
4.1 Pull out like factors :
3x2 - 24xy + 48y2 = 3 • (x2 - 8xy + 16y2)
Trying to factor a multi variable polynomial :
4.2 Factoring x2 - 8xy + 16y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (x - 4y)•(x - 4y)
step4: Detecting a perfect square
4.3 x2 -8xy +16y2 is a perfect square
It factors into (x-4y)•(x-4y) which is another way of writing (x-4y)2
which is another way of writing (x-4y)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 termsFinal result : 3 • (x - 4y)2