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
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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
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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