Solve by factoring Solve by factoring and also solve the las

Solve by factoring and also solve the last question 16x^2 - 25 1000x^3 + 1 64a^3 - 27b^3 81x^2 + 49y^2 16x^2 - 3x = 0 9x^2 + 7 = -24x Solve the problem. The width of a rectangle is 6 kilometers less than twice its length. If its area is 216 square kilometers, find the dimensions of the rectangle.

Solution

1) 16x^2 - 25

applying difference of squares formula

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

(4x)^2 - 5^2 = (4x-5)(4x+5)

2) 1000x^3 + 1

applying sum of cubes formula

a^3 + b^3 = (a+b)(a^2 - ab + b^2 )

1000x^3 + 1 = (10x)^3 + 1^3 = (10x+1)(100x^2 - 10x + 1 )

3) 64a^3 - 27b^3

applying difference of cubes formula

a^3 - b^3 = (a-b)(a^2+ab+b^2)

64a^3 - 27b^3 = (4a)^3 - (3b)^3 = (4a-3b) ( 16a^2 + 12ab + 9b^2)

4) 81x^2 + 49y^2

this expression cannot be factored