i. x2 + 5xy + 9xy2 + 45y3 ii. 2y^2x − 10y^2 − x^2y + 5xy iii. x^2 + x − 30 iv. 343x^3 − 1 Factorize these
Question
i. x2 + 5xy + 9xy2 + 45y3 ii. 2y^2x − 10y^2 − x^2y + 5xy iii. x^2 + x − 30 iv. 343x^3 − 1 Factorize these
Solution
i. The given expression is x^2 + 5xy + 9xy^2 + 45y^3. This can be factored by grouping:
x^2 + 5xy + 9xy^2 + 45y^3 = x(x + 5y) + 9y^2(x + 5y) = (x + 9y^2)(x + 5y)
ii. The given expression is 2y^2x − 10y^2 − x^2y + 5xy. This can be factored by grouping:
2y^2x − 10y^2 − x^2y + 5xy = 2y^2(x - 5) - xy(x - 5) = (2y^2 - xy)(x - 5)
iii. The given expression is x^2 + x − 30. This is a quadratic expression and can be factored using the formula for factoring quadratics:
x^2 + x − 30 = (x - 5)(x + 6)
iv. The given expression is 343x^3 − 1. This is a difference of cubes and can be factored using the formula for factoring difference of cubes:
343x^3 − 1 = (7x - 1)(49x^2 + 7x + 1)
Similar Questions
Factorize :i. 3x2y+9xy2–15xy ii. 2222 cb4916ba361 iii. 16x2–24yz–9y2–16z2 iv. (x–2y)2–6(x–2y)+5
Add the following expressions:3x²y + 4x³y – xy² + x²y², 11x²y – x³y + 5x²y², 5x³y – x²y² + 7x²y – 3xy²
Simplify each of the following. Express your answers with positive exponents.a ( )x2 3y43xy ( )xy–2 2x–3y5 b x2y–3( )2xy2 3 y42x–2 c 6a3b24a4b–2 5ab3a–2b a5b–32a–2b__________________ __________________ _______________________________________ __________________ _______________________________________ __________________ _____________________d 5x0 + ( )3x2 0 e ( )4y3 + 3x 0 f ( )12m6n–5 2( )m4n–2 3 ( )m–4n2 –2
Identify terms and their coefficients from the following expressions:(i) 6x2y2 – 9x2y2z2+ 𝐳𝟐𝟒(ii) 6.1x – 5.9xy + 2.3y
Factor and reduce to simplest form.6x2 + 11xy − 10y23x2 + 10xy − 8y2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.