solve this 16a^4x^3+54ay^3
Answers
Answer:
Step 1 :
Equation at the end of step 1 :
((16 • (a^4)) • (x³)) + (2•a)
Step 2 :Equation at the end of step 2 : ( • ) + (2•3³ay³)
Step 3 :Step 4 :Pulling out like terms :
4.1 Pull out like factors :
16a^4 x³ + 54ay³ = 2a • (8a³x³ + 27y³)
Trying to factor as a Sum of Cubes :
4.2 Factoring: 8a³x³ + 27y³
Theory: A sum of two perfect cubes, a³ + b³ can be factored into :
(a+b) • (a²-ab+b²)
Proof : (a+b) • (a²-ab+b²)
= a³-a²b+ab²+ba²-b²a+b³
= a³+(a²b-ba²)+(ab²-b²a)+b³
= a³+0+0+b³
= a³+b³
Check: 8 is the cube of 2
Check: 27 is the cube of 3
Check: a³ is the cube of a^1
Check: x³ is the cube of x^1
Check: y³ is the cube of y^1
Factorization is :
(2ax + 3y) • (4xa²x² - 6axy + 9y²)
Trying to factor a multi variable polynomial :
4.3 Factoring 4a²x² - 6axy + 9y²
Try to factor this multi-variable trinomial using trial and error
→Factorization fails
∴Final result : 2a • (2ax + 3y) • (4a²x² - 6axy + 9y²)
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