factorize the following 25(a-b)²-16(c-d)²
Answers
Step-by-step explanation:
STEP1
Equation at the end of step 1
(25 • ((a - b)2)) - 16 • (c - d)2
STEP2
Equation at the end of step 2
25 • (a - b)2 - 16 • (c - d)2
STEP3
3.1 Evaluate : (a-b)2 = a2-2ab+b2
3.2 Evaluate : (c-d)2 = c2-2cd+d2
Trying to factor by pulling out :
3.3 Factoring: 25a2-50ab+25b2-16c2+32cd-16d2
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -50ab+25a2
Group 2: 32cd-16c2
Group 3: 25b2-16d2
Pull out from each group separately :
Group 1: (a-2b) • (25a)
Group 2: (c-2d) • (-16c)
Group 3: (25b2-16d2) • (1)
Looking for common sub-expressions :
Group 1: (a-2b) • (25a)
Group 3: (25b2-16d2) • (1)
Group 2: (c-2d) • (-16c)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Final result :
25a2 - 50ab + 25b2 - 16c2 + 32cd - 16d2.
As nouns the difference between vaporization and melting
is that vaporization is a conversion of a solid or a liquid into a gas while melting is the process of changing the state of a substance from solid to liquid by heating it past its melting point.