**Ques: Mathematics Identities**

(a+b)^{2} = a^{2} + 2ab + b^{2}

(a-b)^{2} = a^{2} – 2ab + b^{2}

(a^{2}-b^{2}) = (a +b) (a-b)

(a+b)^{3} = a^{3} + b^{3} +3a^{2}b+3ab^{2}

Ques: **Find the LCM and HCF of 135 and 225.**

Here, we will find the LCM and HCF by prime factorization method.

135 = 3 × 3 × 3 × 5 =3^{2} × 5

225 = 3 × 3× 5 × 5 = 3^{2}×5^{2}Therefore,

LCM = 3^{2}×5^{2} =675

and HCF = 3^{2}× 5 = 45

**Ques: What does HCF mean?**

The largest common factor of all the given numbers is known as the Highest Common Factor of the numbers. The highest number that can be divided exactly into two or more numbers without any remainders.

**Ques: What is the HCF (highest common factor)?**

The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers. In simple words, the HCF (Highest Common Factor) of two natural numbers x and y is the largest possible number that divides both x and y. Let us understand this definition using two numbers, 18 and 27.

**Ques: Solutions of linear equation**

**Ques: Formula used in (AP)?**

**Arithmetic Progression (AP)**

- nth term of an AP = a + (n-1) d
- Arithmetic Mean = Sum of all terms in the AP / Number of terms in the AP
- Sum of ‘n’ terms of an AP = 0.5 n (first term + last term) = 0.5 n [ 2a + (n-1) d ]

**Ques: What is the formula to find the common difference of an AP?**

Common difference of an AP: d = a2 – a1.

**Ques: How do you find the nth term of an AP formula?**

Formula of Arithmetic Progression nth term of an AP Formula to find the nth term of an AP is Tn = a + (n – 1) d

**Ques: What is the formula to find the sum of an AP?**

AP = 0.5 n (first term + last term) = 0.5 n [ 2a + (n-1) d ]

**Ques: Formula of circle?**

**Ques: Basic Formula of Triangle?**

**Ques: Lines and angle Formula?**

**Ques: Percentage & it’s application?**

**Ans:- **

**Ques: Introduction of trigonometry formula?**

**Ques: Mensuration all formulas?**