Factorise Difference of Two Squares 2

Years

Try VividMath Premium to unlock full access

Start Free Trial

Time limit: 0

Quiz summary

0 of 4 questions completed

Questions:

Information

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 4

1. Question

Factor.

36 m^{2} - 121 n^{2}

$36m^2-121n^2$

1. $(6 m + 11 n) (6 m - 11 n)$ $(6m+11n)(6m-11n)$
2. $(12 m + 11 n) (3 m - 11 n)$ $(12m+11n)(3m-11n)$
3. $(4 m + 11 n) (9 m - 11 n)$ $(4m+11n)(9m-11n)$
4. $(6 m + 12 n) (6 m - 10 n)$ $(6m+12n)(6m-10n)$

Hint

Help Video

Correct

Exceptional!

Incorrect

Need Text

Play

Current Time 0:00

Duration Time 0:00

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

Video Acceleration:

Off

00:00

Mute

Playback Rate

2x
1.5x
1.25x
1x
0.75x
0.5x

Subtitles

subtitles off

Captions

captions off
English

Chapters

Chapters

Factoring the Difference of Two Squares

a^{2} - b^{2} = (a + b) (a - b)

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$

First, express both terms of the polynomial as perfect squares. In other words, both terms should have

2

$2$ as their exponent.

	$36 m^{2} - 121 n^{2}$ $36m^2-121n^2$
$=$ $=$	${(6 m)}^{2} - 121 n^{2}$ $(6m)^2-121n^2$	${(6 m)}^{2} = 36 m^{2}$ $(6m)^2=36m^2$
$=$ $=$	${(6 m)}^{2} - {(11 n)}^{2}$ $(6m)^2-(11n)^2$	${(11 n)}^{2} = 121 n^{2}$ $(11n)^2=121n^2$

Next, label the values in the expression.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$

$(6m)^2-(11n)^2$

$a=6m$

$b=11n$

Substitute the values into the formula given for Factoring the Difference of Two Squares.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$	$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$
$(\color{#00880A}{6m})^2-(\color{#9a00c7}{11n})^2$	$=$	$(\color{#00880A}{6m}+\color{#9a00c7}{11n})(\color{#00880A}{6m}-\color{#9a00c7}{11n})$

$(6m+11n)(6m-11n)$

Question 2 of 4

2. Question

Factor.

$x^2y^2-z^2$

1. $(y+z)(x-z)$
2. $(xy+z)(y-z)$
3. $(x+z)(y-z)$
4. $(xy+z)(xy-z)$

Hint

Help Video

Correct

Well Done!

Incorrect

Need Text

Play

Current Time 0:00

Duration Time 0:00

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

Video Acceleration:

Off

00:00

Mute

Playback Rate

2x
1.5x
1.25x
1x
0.75x
0.5x

Subtitles

subtitles off

Captions

captions off
English

Chapters

Chapters

Factoring the Difference of Two Squares

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$

First, express both terms of the polynomial as perfect squares. In other words, both terms should have

$2$ as their exponent.

		$x^2y^2-z^2$
	$=$	$(xy)^2-z^2$	$(xy)^2=x^2y^2$

Next, label the values in the expression.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$

$(xy)^2-z^2$

$a=xy$

$b=z$

Substitute the values into the formula given for Factoring the Difference of Two Squares.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$	$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$
$(\color{#00880A}{xy})^2-\color{#9a00c7}{z}^2$	$=$	$(\color{#00880A}{xy}+\color{#9a00c7}{z})(\color{#00880A}{xy}-\color{#9a00c7}{z})$

$(xy+z)(xy-z)$

Question 3 of 4

3. Question

Factor.

$4a^2-9b^2c^2$

1. $(2a+3b)(2a-3c)$
2. $(2a+5bc)(a-4bc)$
3. $(4a+3bc)(a-3bc)$
4. $(2a+3bc)(2a-3bc)$

Hint

Help Video

Correct

Nice Job!

Incorrect

Need Text

Play

Current Time 0:00

Duration Time 0:00

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

Video Acceleration:

Off

00:00

Mute

Playback Rate

2x
1.5x
1.25x
1x
0.75x
0.5x

Subtitles

subtitles off

Captions

captions off
English

Chapters

Chapters

Factoring the Difference of Two Squares

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$

First, express both terms of the polynomial as perfect squares. In other words, both terms should have

$2$ as their exponent.

	$4a^2-9b^2c^2$
$=$	$(2a)^2-9b^2c^2$	$(2a)^2=4a^2$
$=$	$(4a)^2-(3bc)^2$	$(3bc)^2=9b^2c^2$

Next, label the values in the expression.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$

$(2a)^2-(3bc)^2$

$a=2a$

$b=3bc$

Substitute the values into the formula given for Factoring the Difference of Two Squares.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$	$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$
$(\color{#00880A}{2a})^2-(\color{#9a00c7}{3bc})^2$	$=$	$(\color{#00880A}{2a}+\color{#9a00c7}{3bc})(\color{#00880A}{2a}-\color{#9a00c7}{3bc})$

$(2a+3bc)(2a-3bc)$

Question 4 of 4

4. Question

Factor.

$16a^2b^2-81c^2d^2$

1. $(5ab+7cd)(3ab-8cd)$
2. $(12ab+9cd)(4ab-9cd)$
3. $(8ab+9cd)(2ab-9cd)$
4. $(4ab+9cd)(4ab-9cd)$

Hint

Help Video

Correct

Excellent!

Incorrect

Need Text

Play

Current Time 0:00

Duration Time 0:00

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

Video Acceleration:

Off

00:00

Mute

Playback Rate

2x
1.5x
1.25x
1x
0.75x
0.5x

Subtitles

subtitles off

Captions

captions off
English

Chapters

Chapters

Factoring the Difference of Two Squares

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2=(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$

First, express both terms of the polynomial as perfect squares. In other words, both terms should have

$2$ as their exponent.

	$16a^2b^2-81c^2d^2$
$=$	$(4ab)^2-81c^2d^2$	$(4ab)^2=16a^2b^2$
$=$	$(4ab)^2-(9cd)^2$	$(9cd)^2=81c^2d^2$

Next, label the values in the expression.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$

$(4ab)^2-(9cd)^2$

$a=4ab$

$b=9cd$

Substitute the values into the formula given for Factoring the Difference of Two Squares.

$\color{#00880A}{a}^2-\color{#9a00c7}{b}^2$	$=$	$(\color{#00880A}{a}+\color{#9a00c7}{b})(\color{#00880A}{a}-\color{#9a00c7}{b})$
$(\color{#00880A}{4ab})^2-(\color{#9a00c7}{9cd})^2$	$=$	$(\color{#00880A}{4ab}+\color{#9a00c7}{9cd})(\color{#00880A}{4ab}-\color{#9a00c7}{9cd})$

$(4ab+9cd)(4ab-9cd)$

Quizzes

Binomial Products – Distributive Property
Binomial Products – FOIL Method
FOIL Method – Same First Variable 1
FOIL Method – Same First Variable 2
FOIL Method – 3 Terms
Expand Perfect Squares
Difference of Two Squares
Expand Longer Expressions
Highest Common Factor 1
Highest Common Factor 2
Factorise a Polynomial (HCF)
Factorise a Polynomial 1
Factorise a Polynomial 2
Factorise a Polynomial with Integers
Factorise Difference of Two Squares 1
Factorise Difference of Two Squares 2
Factorise Difference of Two Squares 3
Factorise by Grouping in Pairs
Factorise Difference of Two Squares (Harder) 1
Factorise Difference of Two Squares (Harder) 2
Factorise Difference of Two Squares (Harder) 3
Factorise Trinomials (Quadratics) 1
Factorise Trinomials (Quadratics) 2
Factorise Trinomials (Quadratics) 3
Factorise Trinomials (Quadratics) w Coefficient more than 1 (1)
Factorise Trinomials (Quadratics) w Coefficient more than 1 (2)
Factorise Trinomials (Quadratics) w Coefficient more than 1 (3)
Factorise Trinomials (Quadratics) – Complex