How do i solve the following by factorization:

1) 7.7^2-2.3^2
2) 43*56+43*44

I know how to do these manually but not by factorization.

thanks for helping.

To solve the given expressions by factorization, we need to factorize the terms in each expression.

Let's solve each expression step by step:

1) 7.7^2 - 2.3^2:

First, recognize that both terms are perfect squares. We can use the difference of squares formula to factorize the expression:
a^2 - b^2 = (a + b)(a - b)

In this case, a = 7.7 and b = 2.3. Applying the formula, we have:
7.7^2 - 2.3^2 = (7.7 + 2.3)(7.7 - 2.3)

Simplifying further, we get:
(7.7 + 2.3)(7.7 - 2.3) = (10)(5.4) = 54

Therefore, the solution to the expression 7.7^2 - 2.3^2 by factorization is 54.

2) 43*56 + 43*44:

In this case, we need to factor out the common factor 43 from both terms:
43 * 56 + 43 * 44 = 43 * (56 + 44)

Simplifying further, we get:
43 * (56 + 44) = 43 * 100 = 4300

Therefore, the solution to the expression 43*56 + 43*44 by factorization is 4300.

By factorizing the terms in each expression, we were able to obtain a simplified solution for each expression using the given formulas.

these questions have been 'fudged' so that they can be done mentally by using basic factoring techniques.

for the first
7.7^2-2.3^2 , I see the difference of squares
= (7.7 + 2.3)(7.7-2.3)
= 10 (5.4)
= 54

the last one uses 'common factoring'
43*56 + 43*44
= 43(56+44)
= 43*100
= 4300