Multiply: 5y²-7y-15 by 1-y²
By column method
Answers
Answer:
) y − z
(ii)
(iii) z2
(iv)
(v) x2 + y2
(vi) 5 + 3 (mn)
(vii) 10 − yz
(viii) ab − (a + b)
Step-by-step explanation:
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Answer:
(6xy) × (-3x²y³)
= {6 × (-3)} × {xy × x²y³}
= -18x1+2 y1+3
= -18x³y⁴.
(ii) 7ab², -4a²b and -5abc
Solution:
(7ab²) × (-4a²b) × (-5abc)
= {7 × (-4) × (-5)} × {ab² × a²b × abc}
= 140 a1+2+1 b2+1+1 c
= 140a⁴b⁴c.
II. Multiplication of a Polynomial by a Monomial
Rule:
Multiply each term of the polynomial by the monomial, using the distributive law a × (b + c) = a × b + a × c.
Find each of the following products:
(i) 5a²b² × (3a² - 4ab + 6b²)
Solution:
5a²b² × (3a² - 4ab + 6b²)
= (5a²b²) × (3a²) + (5a²b²) × (-4ab) + (5a²b²) × (6b²)
= 15a⁴b² - 20a³b³ + 30a²b⁴.
(ii) (-3x²y) × (4x²y - 3xy² + 4x - 5y)
Solution:
(-3x²y) × (4x²y - 3xy² + 4x - 5y)
= (-3x²y) × (4x²y) + (-3x²y) × (-3xy²) + (-3x²y) × (4x) + (-3x²y) × (-5y)
= -12x⁴y² + 9x³y³ - 12x³y + 15x²y².
III. Multiplication of Two Binomials
Suppose (a + b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.
(a + b) × (c + d)
= a × (c + d) + b × (c + d)
= (a × c + a × d) + (b × c + b × d)
= ac + ad + bc + bd
Note: This method is known as the horizontal method.
(i) Multiply (3x + 5y) and (5x - 7y).
Solution:
(3x + 5y) × (5x - 7y)
= 3x × (5x - 7y) + 5y × (5x - 7y)
= (3x × 5x - 3x × 7y) + (5y × 5x - 5y × 7y)
= (15x² - 21xy) + (25xy - 35y²)
= 15x² - 21xy + 25xy - 35y²
= 15x² + 4xy - 35y².