Question

ws3 qu atics in standard and factored form – multiply po nomials
name:
due date:
#1 what is the standard form? show your work!
a) $(x + 2)(x + 7) =$
d) $(x + 4)(x - 3) =$
b) $(x + 6)(x + 6) =$
e) $(x - 5)(x - 5) =$
c) $(x - 6)(x + 6) =$
f) $(x - 18)(x + 1) =$
#2 write the product in standard form!
a) $(y - 9)(y - 9) =$
d) $(2x + 7)(2x - 7) =$
b) $(a + 10)(a + 10) =$
e) $(x + 4)^2 = (\\_\\_\\_\\_\\_\\_)(\\_\\_\\_
c) $(5x - 3)(5x - 3) =$
f) $(p - 3)^2 =$

Explanation:

#1a Step1: Apply FOIL method

$(x+2)(x+7) = x^2 +7x +2x +14$

#1a Step2: Combine like terms

$x^2 + (7+2)x +14 = x^2 +9x +14$

#1b Step1: Apply FOIL method

$(x+6)(x+6) = x^2 +6x +6x +36$

#1b Step2: Combine like terms

$x^2 + (6+6)x +36 = x^2 +12x +36$

#1c Step1: Apply difference of squares

$(x-6)(x+6) = x^2 -6^2$

#1c Step2: Simplify the constant term

$x^2 -36$

#1d Step1: Apply FOIL method

$(x+4)(x-3) = x^2 -3x +4x -12$

#1d Step2: Combine like terms

$x^2 + (-3+4)x -12 = x^2 +x -12$

#1e Step1: Apply FOIL method

$(x-5)(x-5) = x^2 -5x -5x +25$

#1e Step2: Combine like terms

$x^2 + (-5-5)x +25 = x^2 -10x +25$

#1f Step1: Apply FOIL method

$(x-18)(x+1) = x^2 +x -18x -18$

#1f Step2: Combine like terms

$x^2 + (1-18)x -18 = x^2 -17x -18$

#2a Step1: Apply FOIL method

$(y-9)(y-9) = y^2 -9y -9y +81$

#2a Step2: Combine like terms

$y^2 + (-9-9)y +81 = y^2 -18y +81$

#2b Step1: Apply FOIL method

$(a+10)(a+10) = a^2 +10a +10a +100$

#2b Step2: Combine like terms

$a^2 + (10+10)a +100 = a^2 +20a +100$

#2c Step1: Apply FOIL method

$(5x-3)(5x-3) = 25x^2 -15x -15x +9$

#2c Step2: Combine like terms

$25x^2 + (-15-15)x +9 = 25x^2 -30x +9$

#2d Step1: Apply difference of squares

$(2x+7)(2x-7) = (2x)^2 -7^2$

#2d Step2: Simplify terms

$4x^2 -49$

#2e Step1: Expand square of binomial

$(x+4)^2 = (x+4)(x+4)$

#2f Step1: Apply FOIL method

$(p-3)^2 = (p-3)(p-3) = p^2 -3p -3p +9$

#2f Step2: Combine like terms

$p^2 + (-3-3)p +9 = p^2 -6p +9$

Answer:

#1
a) $x^2 +9x +14$
b) $x^2 +12x +36$
c) $x^2 -36$
d) $x^2 +x -12$
e) $x^2 -10x +25$
f) $x^2 -17x -18$

#2
a) $y^2 -18y +81$
b) $a^2 +20a +100$
c) $25x^2 -30x +9$
d) $4x^2 -49$
e) $(x+4)(x+4)$
f) $p^2 -6p +9$