Answers: _____________________________________________________ Part A) " (3x + 4) " units . _____________________________________________________ Part B) "The dimensions of the rectangle are:
Given: " (9x² + 24x + 16) " ; _______________________________________________________ Let us start with the term: _______________________________________________________
" (9x² + 12x) " ;
→ Factor out a "3x" ; → as follows: _______________________________________
→ " 3x (3x + 4) " ;
Then, take the term: _______________________________________ → " (12x + 16) " ;
And factor out a "4" ; → as follows: _______________________________________
→ " 4 (3x + 4) " _______________________________________ We have:
→ {since the "side length of a square" cannot be a "negative" value.}. ____________________________________________________ → Take the "positive square root of EACH SIDE of the equation; to isolate "s" on one side of the equation; & to solve for "s" ;
→ ⁺√(s²) = ⁺√[(3x + 4)²] '
To get:
→ s = " (3x + 4)" units . _______________________________________________________
Part A):The answer is: "(3x + 4)" units. ____________________________________________________ Explanation for Part B): _________________________________________________________<span>
The area, "A" of a rectangle is:
A = L * w ;
in which "A" is the "area" of the rectangle; "L" is the "length" of the rectangle; "w" is the "width" of the rectangle; _______________________________________________________ Given: " A = </span>(16x² − 25y²) square units" ;
→ We are asked to find the dimensions, "L" & "w" ; → by factoring the given "area" expression completely: ____________________________________________________ → Factor: " (16x² − 25y²) square units " completely '
Note that: "16" and: "25" are both "perfect squares" ;
We can rewrite: " (16x² − 25y²) " ; as:
= " (4²x²) − (5²y²) " ; and further rewrite the expression: ________________________________________________________ Note: ________________________________________________________ " (16x²) " ; can be written as: "(4x)² " ;
→ {Note: We substitute: "(4x)² " for "(16x²)" ; & "(5y)² " for "(25y²)" .} . ; _______________________________________________________ → We have: " (4x)² − (5y)² " ;
→ Note that we are asked to "factor completely" ;
→ Note that: " x² − y² = (x + y) (x − y) " ;
→ {This property is known as the "<u>difference of squares</u>".}.
→ As such: " (4x)² − (5y)² " = " (4x + 5y) (4x − 5y) " . _______________________________________________________ Part B): The answer is: "The dimensions of the rectangle are:
