6 Questions
Expand and simplify: $(5a + 6b)^2$
$25a^2 + 60ab + 36b^2$
Find the square of the binomial: $(8 - 1)$
$64 - 16 + 1$
Which of the binomials will result in the expansion $m^2n^2 + 14mnpq + 49p^2q^2$?
$(mn + 7pq)$
Calculate the square of $(997)$ using an expansion formula.
$994009$
Expand and simplify: $(x + y)(x - y)$
$x^2 - y^2$
Calculate the product of $(3x - 5)(3x + 5)$ using the formula.
$9x^2 - 25$
Study Notes
Expanding Binomials
- The expansion of (a + b)² is (a + b) × (a + b) = a² + 2ab + b².
- The expansion of (a - b)² is (a - b) × (a - b) = a² - 2ab + b².
- The expansion of (a + b) (a - b) is a² - b².
Examples of Expanding Binomials
- (5a + 6b)² = (5a)² + 2(5a)(6b) + (6b)² = 25a² + 60ab + 36b².
- (2p - 39)² = (2p)² - 2(2p)(39) + (39)² = 4p² - 156p + 1521.
- (x - 3)³ = ?
- (ax + by)² = (ax)² + 2(ax)(by) + (by)² = a²x² + 2abxy + b²y².
- (7m - 4)² = (7m)² - 2(7m)(4) + (4)² = 49m² - 56m + 16.
- x + 2 = ?
Identifying Binomials
- The square of the binomial (8 + 1) is 64 + 1 + 16.
- The expansion of m²n² + 14mnpq + 49p²q² is (mn + 7pq)².
Using Expansion Formulas
- (997)² = (1000 - 3)² = (1000)² - 2(1000)(3) + (3)² = 994009.
- (102)² = (100 + 2)² = (100)² + 2(100)(2) + (2)² = 10404.
Multiplying Binomials
- (x + y) (x - y) = x² - y².
- (a + 6) (a - 6) = a² - 36.
- 502 × 498 = (500 + 2) (500 - 2) = (500)² - (2)² = 249996.
- (3x - 5) (3x + 5) = (3x)² - (5)² = 9x² - 25.
- 97 × 103 = (100 - 3) (100 + 3) = (100)² - (3)² = 10000 - 9 = 9991.
- 54 × 46 = (50 + 4) (50 - 4) = (50)² - (4)² = 2500 - 16 = 2484.
- 98 × 102 = (100 - 2) (100 + 2) = (100)² - (2)² = 10000 - 4 = 9996.
Practice binomial expansion problems involving squares and expansions of binomials. Includes finding the square of binomials and expanding expressions with variables. Test your skills with various expansion formulas.
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