Question

17. Evaluate 105 x 109 using the suitable identity​

Answer 1

Step-by-step explanation:

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Answer 2

• As per the data given in the question, we have to find the value of the expression.

               Given data:- $105\times109.$

               To find:- Value of given expression=?

               Solution:-

• Multiplication is denoted by the symbol ($\times$).

• Multiplication is a method to get the product by multiplying two or more values.

• There are six properties of multiplication is given below:-

1. Closure property of multiplication.
2. Commutative property of multiplication.
3. Associative property of multiplication.
4. Distributive property of multiplication over addition.
5. Identity property of multiplication.
6. Zero property of multiplication.

         Therefore,

          $105 \times 109 \\=(100+5)(100+9) \\\quad\left[\text { Using },(\mathrm{x}+\mathrm{a})(\mathrm{x}-\mathrm{b})=\mathrm{x}^{2}+(\mathrm{a}+\mathrm{b}) \mathrm{x}+\mathrm{ab}\right] \\=10000+500+900+45\\=10000+1400+45\\=11445.$

   Hence we will get the value $11445.$