Questions and Answers
Add 7$x^2$ + 11x + 8 and 3$x^2$ - 6x - 7.
10$x^2$ + 5x + 1
Find the product of 5$x^2$y and -3$x^3$y$^2$.
-15$x^5$y$^3$
Find the product of a$^4$b$^2$ and (2a$^2$b)$^3$.
8a$^{10}$b$^4$
Find the product of 3x and 7x + 2.
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Find the product of -5$m^2$ and 4$m^2$ - 2m + 7.
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Simplify: 5$x^3$ + 6$x^2$ + 3x - (-2$x^3$ + 7$x^2$ + 3x - 7)
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Add 3x(7$x^2$ - 5x + 3) and 2(x$^3$ - 4$x^2$ + 5).
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Multiply 2a + 3b by 7a - 5b.
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Multiply (5$a^2$ - 2b) by (2$a^2$ - 3b).
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Find the Square of 9x - 7xy.
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Simplify: a$^2$(b$^2$ - c$^2$) + b$^2$(c$^2$ - a$^2$) + c$^2$(a$^2$ - b$^2$)
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Subtract 4p$^2$q - 3pq + 5pq$^2$ - 8p + 7q - 10 from 18 - 3p - 11q + 5pq - 2pq$^2$ + 5p$^2$q
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Use the identity (x + a)(x + b) = x$^2$ + (a + b)x + ab to find the product of (4x + 5)(4x - 1).
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Use the identity (x + a)(x + b) = x$^2$ + (a + b)x + ab to find the product of (2x + 5y)(2x + 3y).
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Study Notes
Algebraic Expressions and Identities
Section A: Basic Operations
- Adding algebraic expressions: 7x² + 11x + 8 and 3x² - 6x - 7
- Multiplying algebraic expressions: 5x²y and -3x³y², a4b² and (2a²b)³
- Multiplying algebraic expressions: 3x and 7x + 2, -5m² and 4m² - 2m + 7
Section B: Simplification and Expansion
- Simplifying expressions: 5x³ + 6x² + 3x − (−2x³ + 7x² + 3x - 7)
- Adding algebraic expressions: 3x(7x2 – 5x+3) and 2(x3 – 4x2 + 5)
- Multiplying algebraic expressions: 2a + 3b by 7a -5b, (5a² - 2b) by (2a² - 3b)
- Finding the square of an algebraic expression: (9x – 7xy)²
Section C: Advanced Operations and Identities
- Simplifying expressions: a²(b² - c²) + b²(c² - a²) + c²(a² - b²)
- Subtracting algebraic expressions: 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q
- Using identities to find products: (x + a) (x + b) = x2 + (a + b) x + ab, (4x + 5) (4x – 1), (2x + 5y) (2x + 3y)
- Using identities to find products: (2y + 5) (2y + 5), (2a – 7) (2a – 7)
- Simplifying and evaluating an expression: 5a2(a – 2) – 2a3(a + 4) – 5a(a – 2) for a = -1
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