Lana uses factoring by grouping to factor the polynomial 8x2y−10xy2+12x−15y. Her work is shown below, but the last two lines of work are missing.
8x2y−10xy2+12x−15y
(8x2y−10xy2)+(12x−15y)
__[blank 1]__
__[blank 2]__
Select one statement for each blank to correctly complete Lana’s work.
Lana uses factoring by grouping to factor the polynomial 8x2y−10xy2+12x−15y. Her work is shown below, but the last two lines of work are missing.
8x2y−10xy2+12x−15y
(8x2y−10xy2)+(12x−15y)
__[blank 1]__
__[blank 2]__
Select one statement for each blank to correctly complete Lana’s work.
blank 1: 2xy(4x−5y)+3(4x−5y)
blank 1: −4x(2xy+3)+5y(2xy+3)
blank 2: (2xy−3)(4x+5y)
blank 1: −2xy(4x+5y)−3(4x+5y)
blank 2: (2xy+3)(4x−5y)
blank 2: −(2xy+3)(4x−5y)
blank 2: (2xy−3)(4x+5y)
blank 1: −2xy(4x+5y)−3(4x+5y)
blank 2: (2xy+3)(4x−5y)
blank 2: −(2xy+3)(4x−5y)
I believe it is
blank 1: −4x(2xy+3)+5y(2xy+3) and blank 2: (2xy+3)(4x−5y)
8x^2y−10xy^2+12x−15y
= 2xy(4x-5y) + 3(4x-5y)
= (2xy+3)(4x-5y)
Yes, you are correct.
The correct completion for blank 1 is: −4x(2xy+3)+5y(2xy+3)
The correct completion for blank 2 is: (2xy+3)(4x−5y)
That is incorrect. Let's go through the process of factoring by grouping to find the correct answers for the blanks.
To factor the polynomial 8x^2y - 10xy^2 + 12x - 15y using factoring by grouping, we can follow these steps:
Step 1: Group the terms in pairs:
(8x^2y - 10xy^2) + (12x - 15y)
Step 2: Factor out the greatest common factor from each pair:
2xy(4x - 5y) + 3(4x - 5y)
Now, we have two common terms: (4x - 5y).
For blank 1, we need to factor out the common term (4x - 5y) from both grouped terms:
(4x - 5y)(2xy + 3)
For blank 2, we simply write down the factored form from the previous step:
(4x - 5y)(2xy + 3)
So, the correct answers for the blanks are:
Blank 1: (4x - 5y)(2xy + 3)
Blank 2: (4x - 5y)(2xy + 3)