Answer:
21x² -8x -5
Explanation:
You want to develop (5x-2)²-(-2x+3)².
Difference of squares
The pattern for the factoring of the difference of squares is ...
a² -b² = (a -b)(a +b)
Your expression matches this with ...
a = 5x-2
b = -2x+3
So, the factoring is ...
(a -b)(a +b) = ((5x -2) -(-2x +3))·((5x -2) +(-2x +3))
= (5x +2x -2 -3)(5x -2x -2 +3)
= (7x -5)(3x +1)
This product can be found using the distributive property:
= 7x(3x +1) -5(3x +1) = 21x² +7x -15x -5
= 21x² -8x -5
Perfect square trinomial
The pattern for the square of a binomial is ...
(a +b)² = a² +2ab +b²
In the left square, you have ...
so the square is ...
(5x)² +2(5x)(-2) +(-2)² = 25x² -20x +4
In the right square, you have ...
so the square is ...
(-2x)² +2(-2x)(3) +(3)² = 4x² -12x +9
Then the difference of the squares is ...
(25x² -20x +4) -(4x² -12x +9) = (25 -4)x² +(-20 +12)x +(4 -9)
= 21x² -8x -5