Multiply or divide as indicated. r 2 • r • r 5

Elly & Frank Valdez are thinking about buying a new house and financing it through their bank. If they get approved, what ty

Fynjy0 [20]

The loan will most likely be an installment loan. This loan would allow Elly and Frank to make regular payments on the house and simultaneously give them some financially flexibility. They can make small payments or a huge payment depending on their monthly income. These payments are made monthly and can last months or several years. This loan is typical for mortgages, so it would fit the bill in this situation.

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3 years ago

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Which products result in a difference of squares? Select three options. (x minus y)(y minus x) (6 minus y)(6 minus y) (3 + x z)(

ValentinkaMS [17]

Answer:

Third option: $(3 + xz)(-3 + xz)$

Fourth option: $(y^2 - xy)(y^2 + xy)$

Sixth option: $(64y^2 + x^2)(-x^2 + 64y^2)$

Step-by-step explanation:

By definition, we can factor the Difference between two squares:

$a^2 - b^2 = (a+b)(a-b)$

In order to find which products results in a difference of squares, we need to check each option:

$1.\ (x - y)(y - x)=(x)(y)+(x)(-x)-(y)(y)+(-y)(-x)=xy-x^2-y^2+xy=-x^2-y^2+2xy$

The product does not result in a difference of squares.

$2.\ (6 - y)(6 - y)$

Since the signs are equal ( $-$ ), the product will not result in a difference of squares.

Using Distributive Property for the other options, we get:

$3.\ (3 + xz)(-3 + xz)=(3)(-3)+(3)(xz)+(xz)(-3)+(xz)(xz)=\\\\=-9+3xz-3xz+x^2z^2=x^2z^2-9=(xz)^2-(3)^2$

The product results in a difference of squares.

$4.\ (y^2 - xy)(y^2 + xy)=(y^2)(y^2)+(y^2)(xy)-(xy)(y^2)-(xy)(xy)=\\\\=y^4+xy^3-xy^3-x^2y^2=y^4-x^2y^2=(y^2)^2-(xy)^2$

The product results in a difference of squares.

$5.\ (25x - 7y)(-7y + 25x)=(25x - 7y)(25x - 7y)$

Since the signs are equal ( $-$ ), the product will not result in a difference of squares.

$6.\ (64y^2 + x^2)(-x^2 + 64y^2)=(64y^2 + x^2)(64y^2 - x^2)=\\\\=(64y^2)(-x^2)+(64y^2)(64y^2)+(x^2)(-x^2)+(x^2)(64y^2)=\\\\=-64y^2x^2+4096y^4-x^4+64y^2x^2=\\\\=4096y^4-x^4=(64y^2)^2-(x^2)^2$