EXAMPLE 5 Find: (a)(V5? (b) (2/7) (c) (8 - v3) (4)(Vm + 1 + 2)*.27x2(d)StrategyIn part (a), we will use the definition of square root. In part (b), we will use a power rule for exponents. In parts (c) and (d), we will use the FOIL method.WhyPart (a) is the square of a square root, part (b) has the form (xy)", and part (c) has the form (x + y)².Solution(a)(V5)2Because the square of the square root of 5 is 5.(b)We can use the power of a product rule for exponents to find (2V 7x2 ).(2i/72)' = '32°(V7x2)Raise each factor of 27x? to the 3rd power.(Ox )(7x2) Evaluate: 23 = 8. Use(v5)" == a.= 56x2Multiply: 8 ·7 = 56(6) (3 - V3)° - (8 - v3)(8 - v3)2– V3V3(c)Write the base 83 as a factor twice.%D64 – 8V3 - 8/3 + V3 V 3 Use the FOIL method%3D= 64 – 16V3 + 3Combine like radicals: -8/3 - 8/3 = -16/3.= 67 – 16/3Combine like terms: 64 + 3 = 67.Success Tip2(8 - v3)*Sincehas the form (x – y)², we could also use a special product rule to find this square of a difference quickly.(d)We can use the FOIL method to find the product.(/m + 1 + 2)? = (Vm + 1 + 2)(/m + 1 + 2- (vm + 1)*+ 2/ m + 1 + 2/m + 1 + 2· 2== m + 1 + 2/ m + 1 + 2Vm + 1 + X(va)" =Use= a.= m + 4V m + 1 +Combine like terms.

Answered: Image /qna-images/answer/23e5fce5-be40-4339-9b5e-c8e24fd54a98.jpg

EXAMPLE 5 Find: (a) (V5? (b) (2i/7x?) (e) (8- v3)° (d) (Vm+1+2)°. Strategy In part (a), we will use the definition of square root. In part (b), we will use a power rule for exponents. In parts (c) and (d), we will use the FOIL method. Why Part (a) is the square of a square root, part (b) has the form (xy)", and part (c) has the form (x + y)². (V5)? =Ox Solution (а) Because the square of the square root of 5 is 5. (21 7)'. (b) We can use the power of a product rule for exponents to find (21/7)' - 2{(V/7)' Raise each factor of 27x to the 3rd power. (Ox )(7x²) Evaluate: 23 = 8. Use = a. = 56x? Multiply: 8. 7 = 56 () (8 - v3) - (8 - v3)(s - v3) Write the base 8 - V3 as a factor twice. = 64 – 8/3 - 8/3 + /3/3 Use the FOIL method = 64 - 16/3 + 3 = 67 - 16/3 Combine like radicals: -8/3 - 8y3 = -16/3. Combine like terms: 64 + 3 = 67. (8 - v3) Success Tip Since has the form (x - y)?, we could also use special product rule to find this square of a difference quickly. (d) We can use the FOIL method to find the product. (/m + 1 + 2)? = (Vm + 1 + 2)(/m+ 1 + 2) m+ + 2/m + 1 + 2/m + 1 + 2 · 2 %3D = m +1+ 2/ m + 1 + 2/m + 1 +Ox Use = a. = m + 4V m + 1 +| ...... Combine like terms.

EXAMPLE 5 Find: (a) (V5? (b) (2i/7x?) (e) (8- v3)° (d) (Vm+1+2)°. Strategy In part (a), we will use the definition of square root. In part (b), we will use a power rule for exponents. In parts (c) and (d), we will use the FOIL method. Why Part (a) is the square of a square root, part (b) has the form (xy)", and part (c) has the form (x + y)². (V5)? =Ox Solution (а) Because the square of the square root of 5 is 5. (21 7)'. (b) We can use the power of a product rule for exponents to find (21/7)' - 2{(V/7)' Raise each factor of 27x to the 3rd power. (Ox )(7x²) Evaluate: 23 = 8. Use = a. = 56x? Multiply: 8. 7 = 56 () (8 - v3) - (8 - v3)(s - v3) Write the base 8 - V3 as a factor twice. = 64 – 8/3 - 8/3 + /3/3 Use the FOIL method = 64 - 16/3 + 3 = 67 - 16/3 Combine like radicals: -8/3 - 8y3 = -16/3. Combine like terms: 64 + 3 = 67. (8 - v3) Success Tip Since has the form (x - y)?, we could also use special product rule to find this square of a difference quickly. (d) We can use the FOIL method to find the product. (/m + 1 + 2)? = (Vm + 1 + 2)(/m+ 1 + 2) m+ + 2/m + 1 + 2/m + 1 + 2 · 2 %3D = m +1+ 2/ m + 1 + 2/m + 1 +Ox Use = a. = m + 4V m + 1 +| ...... Combine like terms.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter8: Polynomials

Section8.5: Using The Distributive Property

Problem 57PFA

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