Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−54a2b+36ab2−60b2c+150bc2−225c2a+135ca2
Evaluate
(3a−2b)3+(2b−5c)3+(5c−3a)3
Expand the expression
27a3−54a2b+36ab2−8b3+(2b−5c)3+(5c−3a)3
Expand the expression
27a3−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+(5c−3a)3
Expand the expression
27a3−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+125c3−225c2a+135ca2−27a3
The sum of two opposites equals 0
More Steps
Evaluate
27a3−27a3
Collect like terms
(27−27)a3
Add the coefficients
0×a3
Calculate
0
0−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+125c3−225c2a+135ca2
Remove 0
−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+125c3−225c2a+135ca2
The sum of two opposites equals 0
More Steps
Evaluate
−8b3+8b3
Collect like terms
(−8+8)b3
Add the coefficients
0×b3
Calculate
0
−54a2b+36ab2+0−60b2c+150bc2−125c3+125c3−225c2a+135ca2
Remove 0
−54a2b+36ab2−60b2c+150bc2−125c3+125c3−225c2a+135ca2
The sum of two opposites equals 0
More Steps
Evaluate
−125c3+125c3
Collect like terms
(−125+125)c3
Add the coefficients
0×c3
Calculate
0
−54a2b+36ab2−60b2c+150bc2+0−225c2a+135ca2
Solution
−54a2b+36ab2−60b2c+150bc2−225c2a+135ca2
Show Solution
Factor the expression
−3(3a−2b)(3a−5c)(2b−5c)
Evaluate
(3a−2b)3+(2b−5c)3+(5c−3a)3
Simplify
More Steps
Evaluate
(3a−2b)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
(3a)3−3(3a)2×2b+3×3a(2b)2−(2b)3
Calculate
27a3−54a2b+36ab2−8b3
27a3−54a2b+36ab2−8b3+(2b−5c)3+(5c−3a)3
Simplify
More Steps
Evaluate
(2b−5c)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
(2b)3−3(2b)2×5c+3×2b(5c)2−(5c)3
Calculate
8b3−60b2c+150bc2−125c3
27a3−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+(5c−3a)3
Simplify
More Steps
Evaluate
(5c−3a)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
(5c)3−3(5c)2×3a+3×5c(3a)2−(3a)3
Calculate
125c3−225c2a+135ca2−27a3
27a3−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+125c3−225c2a+135ca2−27a3
The sum of two opposites equals 0
More Steps
Evaluate
27a3−27a3
Collect like terms
(27−27)a3
Add the coefficients
0×a3
Calculate
0
0−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+125c3−225c2a+135ca2
Remove 0
−54a2b+36ab2−8b3+8b3−60b2c+150bc2−125c3+125c3−225c2a+135ca2
The sum of two opposites equals 0
More Steps
Evaluate
−8b3+8b3
Collect like terms
(−8+8)b3
Add the coefficients
0×b3
Calculate
0
−54a2b+36ab2+0−60b2c+150bc2−125c3+125c3−225c2a+135ca2
Remove 0
−54a2b+36ab2−60b2c+150bc2−125c3+125c3−225c2a+135ca2
The sum of two opposites equals 0
More Steps
Evaluate
−125c3+125c3
Collect like terms
(−125+125)c3
Add the coefficients
0×c3
Calculate
0
−54a2b+36ab2−60b2c+150bc2+0−225c2a+135ca2
Remove 0
−54a2b+36ab2−60b2c+150bc2−225c2a+135ca2
Evaluate
−54a2b+135a2c−225ac2+36b2a−60b2c+150bc2
Rewrite the expression
−3×18a2b+3×45a2c−3×75ac2+3×12b2a−3×20b2c+3×50bc2
Factor out −3 from the expression
−3(18a2b−45a2c+75ac2−12b2a+20b2c−50bc2)
Factor the expression
More Steps
Evaluate
18a2b−45a2c+75ac2−12b2a+20b2c−50bc2
Calculate
18a2b−45a2c−30acb+75ac2−12b2a+30bac+20b2c−50bc2
Rewrite the expression
3a×6ab−3a×15ac−3a×10cb+3a×25c2−2b×6ab+2b×15ac+2b×10cb−2b×25c2
Factor out 3a from the expression
3a(6ab−15ac−10cb+25c2)−2b×6ab+2b×15ac+2b×10cb−2b×25c2
Factor out −2b from the expression
3a(6ab−15ac−10cb+25c2)−2b(6ab−15ac−10cb+25c2)
Factor out 6ab−15ac−10cb+25c2 from the expression
(3a−2b)(6ab−15ac−10cb+25c2)
−3(3a−2b)(6ab−15ac−10cb+25c2)
Solution
More Steps
Evaluate
6ab−15ac−10cb+25c2
Rewrite the expression
3a×2b−3a×5c−5c×2b+5c×5c
Factor out 3a from the expression
3a(2b−5c)−5c×2b+5c×5c
Factor out −5c from the expression
3a(2b−5c)−5c(2b−5c)
Factor out 2b−5c from the expression
(3a−5c)(2b−5c)
−3(3a−2b)(3a−5c)(2b−5c)
Show Solution