Square DancerTilewrights · polynomials and factoring

A body of four tiles in a perfect square: special products.

Special Products

Special products. In MathBound, the free Algebra I adventure game, Square Dancer asks these problems, and the only way past is to solve them.

Part of Polynomials and Factoring: chapter 8 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Binomial Squares Pattern. Square a binomial with a leading coefficient of 1 using the pattern (a+b)^2 or (a-b)^2.
Product of Conjugates Pattern. Multiply a sum and difference of the same two terms using the difference of squares pattern.

Made by the game’s own question engine. Try each one, then open its steps.

A

student

wrote

(x + 1)^{2} = x^{2} + 1 .

Which

term

did

they

leave

out?

Show the worked steps

$(p + q)^{2} = p^{2} + 2 pq + q^{2} - -$ $the$ $middle$ $term$ $is$ $doubled.$
$(x + 1)^{2}$ $is$ $(x + 1) (x + 1) :$ $the$ $two$ $cross$ $products$ $give$ $2 x .$

Answer: $2 x$

Multiply:

(9 + x) (9 - x)

Show the worked steps

$A$ $sum$ $times$ $a$ $difference$ $of$ $the$ $same$ $two$ $terms$ $leaves$ $no$ $middle$ $term:$ $(p + q) (p - q) = p^{2} - q^{2} .$
$Here$ $p$ $is$ $9$ $and$ $q$ $is$ $x,$ $so$ $the$ $answer$ $is$ $81 - x^{2} .$

Answer: $81 - x^{2}$

What

goes

in

the

box?

(x + 9)^{2} = x^{2} + □ x + 81

Show the worked steps

Answer: $18$

Textbook	Lessons
Standard course	8.3
Big Ideas Math Algebra 1	7.3
Big Ideas Math Algebra 1 (2022)	7.3
Carnegie Learning Algebra I	M5 2.1
CPM Core Connections Algebra	3.2.3
CPS Skyline Algebra	7.3-7.5
enVision Algebra 1	7-3
enVision Algebra 1 (2024)	7-3
Glencoe Algebra 1	8-4
HMH Into Algebra 1	15.3
Holt McDougal Larson Algebra 1	8.3
Illustrative Mathematics Algebra 1	6.8-6.9
Illustrative Mathematics Algebra 1 (v.360)	7.8-7.9
Math Nation Algebra 1 (Florida B.E.S.T.)	2.7, 7.7
Open Up NC Math 1 (MVP)	7.4
OpenStax Elementary Algebra 2e	6.4
Pearson Algebra 1 Common Core	8-4
Reveal Algebra 1	10-4
SpringBoard Algebra 1	25