solve followings by using formula
a) b³+8b²a+16ba²
b)2a³-2a²+1÷2a
Answers
Answer:
Formula for a plus b Whole Square :
In this section, we are going to see the formula/expansion for (a + b)2.
That is,
(a + b)2 = (a + b)(a + b)
(a + b)2 = a2 + ab + ab + b2
(a + b)2 = a2 + 2ab + b2
Proving the Formula for a plus b Whole Square Geometrically
In this section, we are going to see, how to prove the expansion of (a + b)2 geometrically.
We can prove the the expansion of (a + b)2 using the area of a square as shown below.
Formula for a plus b Whole Square - Example Problems
Problem 1 :
Expand :
(x + y)2
Solution :
(x + y)2 is in the form of (a + b)2
Comparing (a + b)2 and (x + y)2, we get
a = x
b = y
Write the formula / expansion for (a + b)2.
(a + b)2 = a2 + 2ab + b2
Substitute x for a and y for b.
(x + y)2 = x2 + 2(x)(y) + y2
(x + y)2 = x2 + 2xy + y2
So, the expansion of (x + y)2 is
x2 + 2xy + y2
Problem 2 :
Expand :
(x + 2)2
Solution :
(x + 2)2 is in the form of (a + b)2
Comparing (a + b)2 and (x + 2)2, we get
a = x
b = 2
Write the formula / expansion for (a + b)2.
(a + b)2 = a2 + 2ab + b2
Substitute x for a and 2 for b.
(x + 2)2 = x2 + 2(x)(2) + 32
(x + 2)2 = x2 + 4x + 9
So, the expansion of (x + 2)2 is
x2 + 4x + 9
1) (a + b)² = a² + 2 ab + b²
(2) (a + b)² = (a - b)² + 4 ab
(3) (a - b)² = a² - 2 ab + b²
(4) (a - b)² = (a + b)² - 4 ab
(5) a² - b² = (a + b) (a - b)
(6) (x+a) (x+b) =x² + (a + b) x+a b
(7) (a+b)³=a³+3a²b+3ab²+b³
(8) (a+b)³=a³+b³+3ab(a+b)
(9) (a-b)³=a³-3a²b+3ab²-b³
(10) (a-b)³=a³-b³-3ab(a-b)
(11) a³+b³ = (a+b)(a²-ab+b²)
(12) a³+b³=(a+b)³-3 ab(a + b)
(13) a³-b³= (a-b)(a²+ab+ b²)
(14) a³-b³=(a-b)³ +3ab(a-b)
(15) (a+b+c)²= a²+b²+c² +2ab+2bc+2ca
(16) (a+b-c)²=a²+b²+c² +2ab-2bc-2ca
(17) (a-b+c)²= a²+b²+c²-2ab-2bc+2ca
(18) (a-b-c)²= a²+b²+c²-2ab+2bc-2ca
(19) a² + b² = (a + b)² - 2ab
(20) a² + b² = (a - b)² + 2ab
(21) a² + b²=½ [(a+b)²-(a-b)²]
(22) ab = ¼[(a+b)²- (a - b)²]
(23) (a + b + c)³ = a³ + b³ + c³ + 3a²b + 3a²c + 3ab² + 3b²c + 3ac² + 3bc² + 6abc
(24) (a + b - c)³ = a³ + b³ - c³ + 3a²b - 3a²c + 3ab² - 3b²c + 3ac² + 3bc² - 6abc
(25) (a - b + c)³ = a³ - b³ + c³ - 3a²b + 3a²c + 3ab²+ 3b²c + 3ac² - 3bc² - 6abc
(26) (a - b - c)³ = a³ - b³ - c³ - 3a²b - 3a²c + 3ab² - 3b²c + 3ac² - 3bc² + 6abc