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spayn [35]
3 years ago
13

Industrustrialization resulted in what changes to america society

History
1 answer:
Setler79 [48]3 years ago
4 0
A system of manufacturing that uses machines to rapidly produce large amounts of a product
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The factor of 2ax^2+4axy+3bx^2+2ay^2+6bxy^+3by^2
grigory [225]

Answer:

2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2= (x+y)^2(2a+3b)

Explanation:

Given

2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2

Required

Factorize

2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2

Rewrite as:

2ax^2+4axy+2ay^2+3bx^2+6bxy+3by^2

Use square parenthesis

[2ax^2+4axy+2ay^2]+[3bx^2+6bxy+3by^2]

Expand each bracket

[2ax^2+2axy+2axy+2ay^2]+[3bx^2+3bxy+3bxy+3by^2]

Factorize each:

[2ax(x+y) + 2ay(x+y)]+[3bx(x+y)+3by(x+y)]

[(2ax+2ay)(x+y)]+[(3bx+3by)(x+y)]

Further, factorize:

(x+y)[(2ax+2ay)]+[(3bx+3by)]

(x+y)[(2ax+2ay)+(3bx+3by)]

Remove bracket

(x+y)[2ax+2ay+3bx+3by]

Reorder:

(x+y)[2ax+3bx+2ay+3by]

Factorize:

(x+y)[x(2a+3b)+y(2a+3b)]

(x+y)[(x+y)(2a+3b)]

Remove square bracket

(x+y)(x+y)(2a+3b)

This gives:

(x+y)^2(2a+3b)

Hence:

2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2= (x+y)^2(2a+3b)

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