Question

using distributive property find the square of 46​

Answer 1

Given : Square of 46

To Find :  Evaluate using Distributive property

Solution:

Square of 46

= 46²

= 46 × 46

= 46 × (50 -  4)

Distributive property

a × ( b ± c) =  a× b ± a × c

= 46 × 50  - 46 × 4

= 2300 - 184

= 2116

Square of 46  = 2116

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Answer 2

$\underline{\textbf{Given:}}$

$\mathsf{46}$

$\underline{\textbf{To find:}}$

$\textsf{Square of 46}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Distributive laws:}}$

$\mathsf{1.\;a{\times}(b+c)=a{\times}b+a{\times}c}$

$\mathsf{2.\;(a+b){\times}c=a{\times}c+b{\times}c}$

$\mathsf{Consider,}$

$\mathsf{46^2}$

$\mathsf{=46{\times}46}$

$\mathsf{=46{\times}(40+6)}$

$\textsf{Using distribitive law (1),}$

$\mathsf{=46{\times}40+46{\times}6}$

$\mathsf{=(40+6){\times}40+(40+6){\times}6}$

$\textsf{Using distribitive law (2),}$

$\mathsf{=40{\times}40+6{\times}40+40{\times}6+6{\times}6}$

$\mathsf{=1600+240+240+36}$

$\mathsf{=1600+516}$

$\mathsf{=2116}$

$\implies\boxed{\mathsf{46^2=2116}}$