## Algebra 8th grade math

**Introduction :**

Let us see about algebra 8th grade math. It is the important section in mathematics in which symbols such as letters of the alphabet stand for numbers. The 8th algebra should contain the equations. This article explains the 8th grade algebra math. It also performs the arithmetic operations. In 8th grade algebra math should contain some basic formulas and algebraic expressions.

Definition:

The combination of words and numbers are called as algebra problems. These types of problems used to solve the equations. There are more important topics covered for the algebra 8th algebra math. The algebra expression is a consequential compilation of numbers, variables, a positive or negative sign of the operations that must makes math and logical sense.

Formulas:

- (a+b)2 = a2+2ab+b2
- (a-b)2=a2-2ab+b2.
- (a+b)(a-b) = a2-b2.
- (a+b)3 = a3-3a2b+3ab2+b3.
- (a-b)3=a3-3a2b+3ab2-b3.
- a3-b3 = (a-b) (a2+ab+b2).
- a3-b3 =(a+b)(a2-ab+b2).
- The quadratic equation is, x= (-b) ±`sqrt(b^2-4*a*c ) / (2 * a)` .
- The nth term in arithmetic progression, tn =a+(n-1)*d.
- The sum of n terms in arithmetic progression is, sn = n/2*(a+1).
- The nth term of a geometric progressive is, tn = a*rn-1.
- The sum of the n terms in geometric progression is, sn= a (1-rn) /(1-r).

**Examples:**

**Problem 1:**

Solve 8th grade algebra problem (2+3)2.

**Solution:**

The given problem like as (a+b)2. Here, a value is 2 and b value is 3.

The formula for (a+b)2 = a2 + b2 + 2ab.

= 22 + 32 + 2*2*3.

= 4+9+12.

= 25.

**Problem 2:**

Solve 8th grade algebra problem (4-6)2.

**Solution:**

The given problem like as (a-b)2. Here a value is 4 and b value is 6.

The formula for (a-b)2 = a2 -2ab+b2.

= 42 – 2*4*6 +62.

=16 – 48 +36.

= 4.

**Problem 3:**

Solve the factor 5x2+8x+4.

**Solution:**

5x2+8x+4 = 5x2+20x+2x+4.

= 5x(x+4) + 2(x+4).

= (x+4) (5x+2).

**Problem 4:**

Solve the 8th grade quadratic equation: 2x2-4x+3 = 0.

**Solution:**

**Given:**a = 2, b = -4 and c = 3.

The formula for quadratic equation is

x = `((-b+- (sqrt(b^2-4ac)) )/(2*a))`

x = ` (-(-4)+-sqrt(-4^2-4*2*3))/ (2*2)`

x =`(4+-sqrt(16-24)) /(2*2)`

x = `(4+-sqrt(-8)) / 4`

x = `(4+-(2isqrt(2))) / 4`

x = 1+ i`sqrt(2) / 2`or 1- i`sqrt(2) / 2`

**Problem 5:**

Solve 8th grade arithmetic progression. Find the nth where 1+2+3…….+50

**Solution:**

The formula for tn =a+(n-1)*d.

a is the initial value. So a = 1.

n is the final value. So n= 50.

d is the difference between two values. So d =1.

Tn = 1+(50-1) *1.

Tn = 1+49.

Tn = 50.