As shown in the figure, in a room, there is a ladder leaning against the wall. The vertical distance Ma between the top of the ladder and the ground is a meter. At this time, the gradient angle of the ladder is 75 degrees. If the bottom of the ladder does not move and the top of the ladder is leaning against the opposite wall, the vertical distance NB between the top of the ladder and the ground is B meter and the gradient angle of the ladder is 45 degrees, then the width ab of the room is () A. A + B2 m B. a − B2 m C. B M D. a m

Factorization method for solving the equation ABX & # 178; - (A & # 178; + B & # 178;) x + AB = 0 (AB ≠ 0)

abx²-（a²+b²）x+ab=0
(ax-b)(bx-a)=0
x1=b/a x2=a/b

How to factorize ABX & # 178; + (A & # 178; + B & # 178;) x + AB?
How to factorize ABX & # 178; + (A & # 178; + B & # 178;) x + AB?

abx² + (a² + b²)x +ab
=abx² + a²x + b²x +ab
=ax(bx+a)+b(bx+a)
=(bx+a)(ax+b)

What is the factorization X & # 178; - 3

x²-3
=X & # 178; - (radical 3) &# 178;
=(x + radical 3) (x-radical 3)
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10a²x²-abx-3b²=0

10a²x²-abx-3b²=0
(5ax-3b)(2ax+b)=0
x=3b/5a,x=-b/2a

If (x ^ 2-ax) - (bx-ab) factorization factor is equal to (x + 1 (X-2), and a < B, then a =, B=

x^2-ax-bx+ab=x^2-(a+b)x+ab=(x-a)(x-b)=(x+1)(x-2)
a

If (X & # 178; - ax) - (BX AB) factorization factor is equal to (x-1) (x + 2), and a < B, find the value of b-a
Calculation by cross phase multiplication

（x²-ax)-（bx-ab)
=x²-(a+b)x+ab
1 -a
\ /
/ \
1 -b
(x²-ax)-(bx-ab)
=(x-a)(x-b)
=(x-1)(x+2)
a＜b
=> a=-2,b=1
=> b-a=3

Factorization of x ^ 2-bx-a ^ 2 + ab

x^2-bx-a^2+ab
=(x^2-a^2)-(bx-ab)
=(x+a)(x-a)-b(x-a)
=(x-a)(x+a-b)

Factorization of ax ^ 2-bx ^ 2 + bx-ax-2a + 2B

The original formula = (AX & # 178; - BX & # 178;) - (AX BX) - (2a + 2b)
=x²(a-b)-x(a-b)-2(a-b)
=(a-b)(x²-x-2)
=(a-b)(x-2)(x+1)

Ax & # 178; - BX & # 178; - BX + ax + 2b-2a x cubic-1 factorization

ax²-bx²-bx+ax+2b-2a
=x²﹙a－b﹚＋x﹙a－b﹚－2﹙a－b﹚
=﹙a－b﹚﹙x²＋x－2﹚
=﹙a－b﹚﹙x＋2﹚﹙x－1﹚
x³－1
=﹙x－1﹚﹙x²＋x＋1﹚