Grade 08 Mathematics: Factoring Polynomials with Difference of Two Squares

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https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph 85.87 cm jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares How can I factor polynomials with difference of two squares? LESSON 002

A.Unlocking Key Concepts DIFFERENCE OF TWO SQUARES

A.DIFFERENCE

The operation involved between terms should be subtraction.

B. TWO

There are only TWO terms in a polynomial involved.

C.

The terms can be expressed in a form of ����, where n is even

85.87 cm jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares
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SQUARES
GENERAL DEFINITION ������ = ������ 2 ������ = ���� �� 2 2 TRY THESE! a. 16��2 b. 25��4 c. 11��8

15 50= 25∙2 = 25∙ 2=5 2

GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com ANSWERS: TRY THESE! WHAT IS SQUARE ROOT? REMEMBER The square root of a number is defined as the value, which gives the number when it is multiplied by itself While the square root of a variable is defined as a variable with half of its exponent
Concepts EXAMPLES: 25=5 ��4 =��2 16��2 =4�� 7= 7 10��4 = 10��2 8��6 =2 2��3 90��10 =3 10��5 160��20 =4 10��10 a. 16��2 b. 25��4 c. 11��8 = 16=4 = ��2 =��1 =�� = 25=5 = ��4 =��2 = 11= 11 = ��8 =��4 4�� 2 5��2 2 11��4 2 THINGS TO REMEMBER 25=5 15=3.87…
A.Unlocking Key
15=
https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares A.Unlocking Key Concepts THINGS TO REMEMBER ��6 =��3 �� 10 =��−5 ��4��2 =��2�� ��10 =��5 ��5 =�� 5 2 �� 7 =�� 7 2 ��5 = ��5 ��−7 = ��−7 B.Introducing New Concepts NEW CONCEPTS Identifying Polynomials with Difference of Two Squares
GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com B.Introducing New Concepts EXAMPLES TRY THESE! GIVEN IS IT A BINOMIAL? CAN BOTH TERMS BE CONVERTED INTO A SQUARE? IS THE FIRST TERM POSITIVE AND THE OTHER TERM NEGATIVE, OR VICE VERSA? CAN YOU USE TECHNIQUE NUMBER 2? 49��2 25 121��2 25 169��2 −9 49��2 +81 9��2 +25 49��2 +9 ��3 +4 ��2 +��3 100��2 1 4��4 ��6

Factoring Polynomials with Difference of Two Squares

https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares
GIVEN IS IT A BINOMIAL? CAN BOTH TERMS BE CONVERTED INTO A SQUARE? IS THE FIRST TERM POSITIVE AND THE OTHER TERM NEGATIVE, OR VICE VERSA? CAN YOU USE TECHNIQUE NUMBER 2? 49��2 25 YES YES YES YES 121��2 25 YES YES YES YES 169��2 9 YES YES YES YES 49��2 +81 YES YES NO NO 9��2 +25 YES YES YES YES 49��2 +9 YES YES NO NO ��3 +4 YES NO NO NO ��2 +��3 YES NO NO NO 100��2 −1 YES YES YES YES 4��4 ��6 YES YES YES YES
B.Introducing New Concepts ANSWER KEY TRY THESE!
the binomial, where the first term should be POSITIVE, and the second term should be NEGATIVE (��2 ��2) POSITIVE NEGATIVE The factors of this type of polynomial will always be in this form: (___ + ___) (___ - ___) ADDITION SYMBOL SUBTRACTION SYMBOL Prepare your Answer
2 Take the square roots of both the terms regardless of the symbol (positive or negative) Take the Square Roots
(��2 ��2) ��2 ��2 ��2 ��2 �� �� = = Finalized Your Answer
4 Place the square root of the positive term on the first blanks in Step 2, and the square root of the negative term on the remaining blanks (___ + ___) (___ - ___) ��2 �� = ��2 �� = �� �� �� ��
Arrange the variables STEP 1 Arrange
STEP
STEP 3
STEP
GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares B.Introducing New Concepts EXAMPLE NO. 1 TRY THESE! 49��2 25 =( + )( − ) = 49��2 =�� = 25=5 =(��+5)(��−5) =49��2 −25 EXAMPLE NO. 2 EXAMPLE NO. 3 https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com −1+100��2 =( + )( − ) = 100��2 =10�� = 1=1 =(10��+1)(10�� 1) =100��2 1 -16��2��10 +4��2��4 =4��2��4 16��2��10 =( + )( − ) = 4��2��4 =2����2 = 16��2��10 =4����5 = 2����2 −4����5 2����2 −4����5

B.Introducing New Concepts

https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares
Factoring Polynomials with Difference of Two Squares EXAMPLES TRY THESE! 2��2 18 196��2 144 2��4��−72��4�� 125��4 20��4 216��4���� 6��5�� 4��4��−36��4�� =2(��2 −9) =2(�� 3)(��+3) =4(49��2 36) =4(7��−6)(7��+6) =2��(��4 −36��4) =2��(��2 6��2)(��2 +6��2) =5 25��4 4��4 =5 5��2 −2��2 5��2 +2��2 =6����(36��4 −��4) =6���� 6��2 −��2 6��2 +��2 =��(4��4 −36��4) =��(2��2 −6��2)(2��2 +6��2)
Examples ACTIVITY
Given Factors 1. 9��2 1 2. 4��2 49 3. 36��2 1 4. ��2 36 5. 180��2 5 6. 294��2 150 7. 150��2 216 8. 20��2 45 9. 3��2 75 10. 24��3 54�� Given Factors 11. ��2 25��2 12. 6��2 96��2 13. ��2 9��2 14. 54��2 6��2 15. 36��4 25��4 16. 4��4 144��4 17. 7��4 28��4 18. 7��4 343��4 19. 16��6 ��6 20. 64��6 ��6 GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com
C. More
TRY THESE!
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08
Factoring Polynomials with
Two Squares
jmathsph@gmail.com GRADE
MATHEMATICS: ALGEBRA
Difference of
Given Factors 1. 9��2 1 (����+��)(���� ��) 2. 4��2 49 (����+��)(���� ��) 3. 36��2 1 (����+��)(���� ��) 4. ��2 36 (��+��)(�� ��) 5. 180��2 5 ��(����+��)(���� ��) 6. 294��2 150 ��(����+��)(���� ��) 7. 150��2 216 ��(����+��)(���� ��) 8. 20��2 45 ��(����+��)(���� ��) 9. 3��2 75 ��(��+��)(�� ��) 10. 24��3 54�� ����(����+��)(���� ��) Given Factors 11. ��2 25��2 (��+����)(�� ����) 12. 6��2 96��2 ��(��+����)(�� ����) 13. ��2 9��2 (��+����)(�� ����) 14. 54��2 6��2 ��(����+��)(���� ��) 15. 36��4 25��4 (������ +������)(������ ������) 16. 4��4 144��4 ��(���� +������)(���� ������) 17. 7��4 28��4 ��(���� +������)(���� ������) 18. 7��4 343��4 ��(���� +������)(���� ������) 19. 16��6 ��6 (������ +����)(������ ����) 20. 64��6 ��6 ������ +���� ������ ����
C. More Examples ACTIVITY TRY THESE!
85.87 cm GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Difference of Two Squares How can I factor polynomials with difference of two squares? LESSON 002 Written, Prepared, and Edited by: John Michael s. cariazo, lpt https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com

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