Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
Simplify the following expression: (a+2b−c)(b−c)+(a−c)2b+b2
3b2+3ab−5bc−ac
2b2+3ab−4bc+c
3ab−5bc−ac−2abc
3b2+c2+3ab−5bc−ac
3b2+c2+3ab−5bc−ac
Plug in small values like a=1,b=1,c=1. The expression becomes (1+2-1)(1-1) + (1-1)2 + 1 = 0 + 0 + 1 = 1. Testing options with a=1,b=1,c=1 identifies Option D as the match (3+1+3−5−1=1).
An algebraic expression: (a + 2b - c)(b - c) + (a - c)2b + b²
(x+y)(z+w)=xz+xw+yz+yw
Plug in small values like a=1,b=1,c=1. The expression becomes (1+2-1)(1-1) + (1-1)2 + 1 = 0 + 0 + 1 = 1. Testing options with a=1,b=1,c=1 identifies Option D as the match (3+1+3−5−1=1).
Forgetting the negative sign when distributing the product of two binomials involving a negative variable like −c.
Expand the first term
Expanding (a+2b−c)(b−c) by multiplying each term: a(b−c)+2b(b−c)−c(b−c)
ab−ac+2b2−2bc−bc+c2=ab−ac+2b2−3bc+c2
Expand the second and third terms
Expanding (a−c)2b gives 2ab−2bc, then adding b2 to the total.
(2ab−2bc)+b2
Combine all terms
Summing the results: (ab−ac+2b2−3bc+c2)+(2ab−2bc)+b2
(ab+2ab)+(2b2+b2)+c2−(3bc+2bc)−ac
Final simplification
Grouping like terms to get the final simplified polynomial.
3ab+3b2+c2−5bc−ac
D is correct because expanding and combining like terms yields the result 3b2+c2+3ab−5bc−ac.
This type of simplification is fundamental to solving higher-degree equations and coordinate geometry problems in competitive exams.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants