Expand the following expressions: (x−4)(x+4), (x−7)2, (y+3)2.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems.

For $(x-4)(x+4)$ :

Recognize the pattern as a difference of squares, $(a-b)(a+b) = a^2 - b^2$ .
Here, $a=x$ and $b=4$ .
$(x-4)(x+4) = x^2 - 4^2$
Calculate the squared term.
$x^2 - 4^2 = x^2 - 16$
The expanded form is:
$\boxed{x^2 - 16}$
For $(x-7)^2$ :
Expand the squared term using the formula $(a-b)^2 = a^2 - 2ab + b^2$ .
Here, $a=x$ and $b=7$ .
$(x-7)^2 = x^2 - 2(x)(7) + 7^2$
Simplify the terms.
$x^2 - 14x + 49$
The expanded form is:
$\boxed{x^2 - 14x + 49}$
For $(y+3)^2$ :
Expand the squared term using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .
Here, $a=y$ and $b=3$ .
$(y+3)^2 = y^2 + 2(y)(3) + 3^2$
Simplify the terms.
$y^2 + 6y + 9$
The expanded form is:
$\boxed{y^2 + 6y + 9}$

Expand the following expressions: (x-4)(x+4), (x-7)2, (y+3)2.