...results are the same from both operations, (68 = 68), we say that the work "checks." Rule. In multiplying a polynomial by a monomial, multiply each term of the polynomial by the monomial and ivrite the successive products in a new polynomial, each u.ith its proper sign. Exercise 29 Perform...

...= 36, or we may say 6-3-2 = 6-6 = 36. This is called the associative laio of multiplication. Law 3. To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial, and write the results in succession with their proper signs. For example, x(a-\-V) = ax-\-ab; 7a(2a —...

...From the above problem a rule for multiplication of a polynomial by a monomial can be stated: Rule. To multiply a polynomial by a monomial multiply each term of the polynomial by the monomial. EXERCISE 8 Multiply: 1. <z2+3a6+462 by 5. Ans. 5a2+15ab+2062. 2. x2-3xy+4y2 by 5x. 5x3-15x2y+2Qxy2....

...35 + 15 = 50 b. 6(4 + 5) = (6 X 4) + (6 X 5) = 24 + 30 = 54 c. a(b + c + d) = ab + ac + ad Rule. — To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial and combine the results. Example. — Multiply 3 a2 - 2 ab + 62 by - 3 ab. Solution. — (- 3 a6) X (3...

...x ( 2a+4b) = ( 2a+4b) + ( 2a+4b) + (2a+4b) =6a+ 12b. From cases such as these, it is evident that: To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial. 231. Multiplication of a Polynomial by a Polynomial. 31 3 tens+1 22 2 tcns+2 62 6 tens+2 62 6 (tens)...

...exponent equal to the sum of the powers: !Ха3 = а'; я262Хай = а3&3; — 7aftX2ac= — 14a2ftc. To multiply a polynomial by a monomial, multiply each term of the olynornial Ъу the monomial and add the partial products: (60 — 3ft)x3c=8ac-9ftc. To multiply two...

...The preceding exercises suggest the following rule for multiplying a polynomial by a monomial. RULE. To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial and combine the partial products. Find the following products : 7. 4(2 / - 3 *) . 8. 5(6 x - 4) 9. 6(2...

...exponents of that letter in the multiplicand and the multiplier. 10. Multiplication by a Monomial. — To multiply a polynomial by a monomial, multiply each term of the multiplicand in succession by the multiplier, observing the laws of signs and exponents already stated,...

...5 x3 - 6 x2y - 7 xy2 + 2 y3 4 a2 — 3 xy2 12 a3 - 8 a2b - 15 xУ + 18 xtys + 21 ofy* - 6 xy5 Rule. To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial and add the products. Multiplication may be expressed by means of parentheses. Thus, 5 ab(a2 — ab + b2)...

...of exponents for multiplication. Illustration. (16 xy3) ( - 2 xгy) = - 32(xy*) (x*y) = - 32 tfy*. To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial and combine the results. Illustration. 5 x(3 x3 - 4 у - 5 z) = 15 x4 - 20 xy - 25 xz. To multiply a polynomial...