Simplify each expression.?

Question

please help me simplify each expression. and please show all work.

(3x - 4)^2 - (2x + 3)^2

Answer 1

Using the formula for the square of a binomial.

(3x-4)^2 = 9x^2-24x+16 and (2x+3)^2 = 4x^2+12x+9, then

(3x-4)^2 - (2x+3)^2 = 9x^2-24x+16-4x^2-12x-9 , which simplifies to

5x^2-36x+7

Answer 2

we know

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

so (3x-4)^2 - (2x +3)^2 = (3x-4 + 2x + 3)(3x-4 - 2x - 3)

=(5x -1)(x-7)

Answer 3

9x2 - 24x + 16 - 4x2 -12x - 9 = 5x2 - 36x + 7 = (5x - 1)(x - 7)

Answer 4

(3x - 4)^2 - (2x + 3)^2

This expression is of the form: (a^2 - b^2) whose factors are (a + b)(a - b)

where: a = 3x - 4

b = 2x + 3

Therefore:

(3x - 4)^2 - (2x + 3)^2

= [(3x - 4) + (2x + 3)][[(3x - 4) - (2x + 3)]

=(3x - 4 + 2x + 3)(3x - 4 - 2x - 3)

= (3x + 2x - 4 + 3)(3x - 2x - 4 - 3)

= (5x - 1)(x - 7)