Question

question 1-4
match each polynomial with a factoring technique. if none of the techniques can be used to factor the polynomial, select none.

	factor by grouping	difference of squares	perfect square trinomial	none
$16m^2 + 40mn + 25n^2$	$\square$	$\square$	$\square$	$\square$
$64d^2 + 9$	$\square$	$\square$	$\square$	$\square$
$9a^2 - 36b^2$	$\square$	$\square$	$\square$	$\square$

Explanation:

Step 1: Analyze \(8xy + 4y + 10x + 5\)

Factor by grouping: Group terms as \((8xy + 4y)+(10x + 5)\). Factor out \(4y\) from the first group and \(5\) from the second: \(4y(2x + 1)+5(2x + 1)=(4y + 5)(2x + 1)\). So it uses Factor by grouping.

Step 2: Analyze \(16m^{2}+40mn + 25n^{2}\)

Check if it's a perfect square trinomial. \(16m^{2}=(4m)^{2}\), \(25n^{2}=(5n)^{2}\), and \(40mn = 2\times4m\times5n\). So \((4m + 5n)^{2}\), uses Perfect square trinomial.

Step 3: Analyze \(64d^{2}+9\)

Difference of squares is \(a^{2}-b^{2}\), but this is \(a^{2}+b^{2}\), can't be factored with given techniques. So None.

Step 4: Analyze \(9a^{2}-36b^{2}\)

First factor out 9: \(9(a^{2}-4b^{2})\), then \(a^{2}-4b^{2}=(a - 2b)(a + 2b)\) (difference of squares). So uses Difference of Squares.

Answer:

Polynomial	Factor by grouping	Difference of Squares	Perfect square trinomial	None
\(16m^{2}+40mn + 25n^{2}\)			✔️
\(64d^{2}+9\)				✔️
\(9a^{2}-36b^{2}\)		✔️