Elementary Algebra - Problem Drill 18: Multiplying and Dividing Polynomials

Transcription

1 Elementary Algebra - Problem Drill 18: Multiplying and Dividing Polynomials No. 1 of Simplify the expression -2a(3m n + 7mn). (A) -6am + 2an + 14amn (B) 6am + 2an 14amn (C) -6am + 2an 14amn (D) -6am + 2n 14amn (E) -6am 2an + 14amn Use the distributive property to simplify the expression. Use the distributive property to simplify the expression. C. Correct! You multiplied -2a by each term inside the parentheses to simplify the expression. Use the distributive property to simplify the expression. Use the distributive property to simplify the expression. Use the distributive property to simplify the expression. 2a(3m n + 7mn) = -2a(3m) 2a(-n) 2a(7mn) = -6am + 2an 14amn (C) -6am + 2an - 14amn

2 No. 2 of Simplify the expression mnx y mn x y (A) -9m 2 n 5 x -8 y 12 (B) -6m 2 n 5 x -8 y 12 (C) -9m 2 nx -8 y -2 (D) 9m 2 n 5 x -8 y 12 (E) 6m 2 nx 4 y 2 A. Correct! You divided each factor from numerator by the like factor from the denominator to reach the final answer. Divide each factor from numerator by a like factor from the denominator to reach the final answer. Divide each factor from numerator by a like factor from the denominator to reach the final answer. Divide each factor from numerator by a like factor from the denominator to reach the final answer. Divide each factor from numerator by a like factor from the denominator to reach the final answer. Divide each factor from numerator by a like factor from the denominator to reach the final answer. 63mnx y 7 mn x y = 9m n x y = 9mnx y (A) -9m 2 n 5 x -8 y 12

3 No. 3 of The dimensions of a rectangle are (3mn + 1) and (4mn 1). What is the area of the rectangle? (A) m 2 n 2 + mn 1 (B) 12m 2 n 2 + 7mn 1 (C) 12m 2 n 2 + mn 1 (D) 12m 2 n 2 + mn + 1 (E) 14mn Find the area of a rectangle by multiplying its length times its width. Find the area of a rectangle by multiplying its length times its width. C. Correct! You multiplied (3mn + 1) by (4mn 1) and simplified to get the area of the rectangle. Find the area of a rectangle by multiplying its length times its width. Find the area of a rectangle by multiplying its length times its width. Find the area of a rectangle by multiplying its length times its width. Area = (3mn + 1)(4mn 1) 2 2 = 12m n 3mn + 4mn = 12mn + mn 1 (C) 12m 2 n 2 + mn - 1

4 No. 4 of What is the product (3x 2y) 2? (A) 9x 2 6xy + 4y 2 (B) 3x 2 12xy + 4y 2 (C) 9x 2 12xy + 4y 2 (D) 9x 2 12xy + 2y 2 (E) 6x 4y Review the identity for squaring the difference of two monomials. Review the identity for squaring the difference of two monomials. C. Correct! You used the binomial identity to expand the product. Review the identity for squaring the difference of two monomials. Review the identity for squaring the difference of two monomials. The square of the difference of two monomials equals the sum of the squares of the monomials minus twice their product. (3x 2y) 2 = (3x) 2 2(3x)(2y) + (2y) 2 = 9x 2 12xy + 4y 2 (C) 9x 2-12xy + 4y 2

5 No. 5 of The dining room of Julie s house is 121ax 2 y 6 z 2 square feet. The width of the room is 11axy 4 feet. What is the length of the dining room? (A) 121xy 2 z 2 (B) 110xy 2 z 2 (C) 11axy 2 z 2 (D) 11xy 2 z 2 (E) 11xy 2 length of the room. length of the room. length of the room. D. Correct! You divided the area by the width to find the length. length of the room. length of the room. (121ax 2 y 6 z 2 )/(11axy 4 ) = (121/11)(a/a)(x 2 /x)(y 6 /y 4 )(z 2 ) = 11xy 2 z 2 (D) 11xy 2 z 2

6 No. 6 of Simplify the expression ( 132x 6 yz x 6 y 4 z 3 99x 2 y 3 z 4 ) 11xyz. (A) -11x 5 yz x 5 y 3 z 2 9xy 2 z 3 (B) -11x 5 z x 5 y 3 z 2 9xy 2 z 3 (C) -12x 5 z x 6 y 3 z 2 9xy 2 z 3 (D) -12x 5 z x 5 y 3 z 2 99xy 2 z 3 (E) -12x 5 z x 5 y 3 z 2 9xy 2 z 3 Divide each term of the polynomial by the monomial. Divide each term of the polynomial by the monomial. Divide each term of the polynomial by the monomial. Divide each term of the polynomial by the monomial. E. Correct! You divided each term of the dividend by the divisor. Divide each term of the polynomial by the monomial. ( 132x 6 yz x 6 y 4 z 3 99x 2 y 3 z 4 ) 11xyz ( 131x 6 yz 3 11xyz ) + (121x 6 y 4 z 3 11xyz ) (99x 2 y 3 z 4 11xyz) -12x 5 z x 5 y 3 z 2 9xy 2 z 3 (E) -12x 5 z x 5 y 3 z 2-9xy 2 z 3

7 No. 7 of x yz 9mn 27my 7. Simplify the expression. 81mn z 7 x 5n (A) 3m 5 x 2 y 12 (B) 3m 5 x 2 y 12 z 2 (C) 3m 5 n 2 x 2 y 12 (D) 9m 5 x 2 y 12 (E) 9 m 5 n 2 x 2 y 12 A. Correct! You canceled the common factors in the numerator and denominator then simplified. Cancel the common factors in the numerator and denominator to simplify. Cancel the common factors in the numerator and denominator to simplify. Cancel the common factors in the numerator and denominator to simplify. Cancel the common factors in the numerator and denominator to simplify. Cancel the common factors in the numerator and denominator to simplify. 35x yz 9mn 27mxy xyz mn mxy = mn z 7 x 5n z mn z x n x = 3mxy (A) 3m 5 x 2 y 12

8 No. 8 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on 12paper as 8. Simplify the expression (mn 3x)(mn + 4y). (A) m 2 n 2 + 4mny 3mnx + 12xy (B) m 2 n 2 + mny 3mnx 12xy (C) m 2 n 2 + 4mny mnx 12xy (D) m 2 n 2 + 4mny 3mnx 12xy (E) 2mn 7xy Use the FOIL method to simplify the expression. Use the FOIL method to simplify the expression. Use the FOIL method to simplify the expression. D. Correct! You multiplied the binomials using the FOIL method. Use the FOIL method to simplify the expression. Use the FOIL method to simplify the expression. (mn 3x)(mn + 4y) = (mn) 2 + mn(4y) + (-3x)(mn) + (-3x)(4y) = m 2 n 2 + 4mny 3mnx 12xy (D) m 2 n 2 + 4mny - 3mnx - 12xy

9 No. 9 of The area of a rectangle is expressed by 142m 3 n 4 x 5 y 7 and its width is expressed by 71x 2 y 3. Which term describes its length? (A) 2m 3 n 4 x 3 y 4 (B) 2m 3 n 4 x 7 y 10 (C) 4m 3 n 4 x 3 y 3 (D) 4m 3 n 4 x 2 y 4 (E) 4m 3 n 4 x 2 y 3 A. Correct! You divided the area by the width. length of the rectangle. length of the rectangle. length of the rectangle. length of the rectangle. length of the rectangle. Length = (142m 3 n 4 x 5 y 7 ) (71x 2 y 3 ) = 2m 3 n 4 x 3 y 4 (A) 2m 3 n 4 x 3 y 4

10 No. 10 of Which is the area of the shaded region? (A) 2abcd (B) 6abcd (C) 12abcd (D) 18abcd (E) 36abcd Subtract the area of the inner rectangle from the area of the outer rectangle. B. Correct! You subtracted the area of the inner rectangle from the area of the outer rectangle. Subtract the area of the inner rectangle from the area of the outer rectangle. Subtract the area of the inner rectangle from the area of the outer rectangle. Subtract the area of the inner rectangle from the area of the outer rectangle. Subtract the area of the inner rectangle from the area of the outer rectangle. The area of the shaded region = (3ab)(4cd) (2ac)(3bd) = 12abcd 6abcd = 6abcd (B) 6abcd