Question

97 × 101 distributive property .​

Answer 1

Step-by-step explanation:

97×101

(100-3)(100+1)

(100)^2-(3+1)100-3×1

10000-400-3

9597

Answer 2

Answer:

Concept:

To "distribute" anything is to divide it up or to give someone a piece of it. The distributive property states that combining the products together after multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend separately by the number.

Step-by-step explanation:

• $97 \times 101$ $=9797$   ⇒ A                     ( by direct method)
• The distributive property aids in solving difficult problems. An expression  can be recasted by distributing or dividing a factor as the sum or difference of two numbers using the distributive principle of multiplication.

• By distributive property,

                       $p \times (q+r)= (p \times q) + (p \times r)$

• The given product of two numbers can be written as,

                  $97 \times 101 = 97 \times (100+1)$

                                 $= (97 \times 100) + ( 97 \times 1)$

                                 $=9700+97$

                                  $=9797$              ⇒    B          

From A and B , it is proved distributive property holds.

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