Question

Which polynomial identity will prove that 49 - 4 = 45?

A. Difference of Squares B. Difference of Cubes C. Sum of Cubes D. Square of a Binomial

Answer 1

49 - 4 = 45
7² - 2² = 45
a² - b² = ( a + b ) ( a - b ) - difference of squares
( 7 - 2 ) · ( 7 + 2 ) = 45
5 · 9 = 45
45 = 45
Answer: A ) Difference of Squares

Answer 2

Option A is correct

Difference of squares identity should be used to prove 49-4 =45

Explanation:

Prove that : 49 - 4 = 45

Polynomial identities are just equations that are true, but identities are particularly useful for showing the relationship between two apparently unrelated expressions.

Difference of the squares identity:

`a^2-b^2 = (a-b)(a+b)`

Take LHS

49 - 4

We can write 49 as
`7 * 7 =7^2` and 4 as
`2 * 2 =2^2`.

then;

`49 - 4 = 7^2 -2^2`

Now, use the difference of square identity;

here a =7 and b = 2

`7^2-2^2 = (7-2) \cdot (7+2)`

or

`7^2-2^2 = 5 \cdot 9 = 45` = RHS proved!

therefore, the difference of square polynomial identity should be used to prove that 49-4 =45