Algebraic rules questions?

Question

how do i evaluate 905^2 - 95^2 using suitable algebraic rules?

what about 38*62+38^2 and 69*45+45*31

Answer 1

Favorite Answer

a^2 – b^2 = (a + b)(a – b)

905^2 – 95^2 = (905 + 95)(905 – 95)

= 1000 × 810 = 810000

(a × b) + (a × c) = a(b + c)

38 × 62+38 × 38

= 38(62 + 38)

= 38(100) = 3800

69 × 45 + 45 × 31

= 45(69 + 31)

= 45 × 100 = 4500

Answer 2

905^2-95^2 = (905+95)(905-95) = 1000*810 = 810,000

38*62+38^2 = 38(62+38) = 38(100) = 3,800

69*45 + 45*31 = 45(69+31) = 45*100 = 4500

Answer 3

905^2 - 95^2

diff of two squares

(905 - 95)(905+95)

(810)(1000)=810000

(38)62+38^2

(38)(62)+(38)(38)

(38)(38+62)

38*100=3800

69*45 +45*31

45*(69+31)

45*100

4500

Answer 4

Not sure I would call that algebra, more like arithmetic, but I suppose you could do something like:

(905)^2 -95 ^2 -->

((1000-95)^2 -95^2 -->

(1000)^2 -2*(95)(1000) +95^2 -95^2 -->

I will leave the rest to you :)

Source(s): Math degree from top university