We Distribute, Yet Things Multiply – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash Part I, tailored for Class 8 in Mathematics.
This one-pager compiles key formulas and equations from the We Distribute, Yet Things Multiply chapter of Ganita Prakash Part I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
a(b + c) = ab + ac
a, b, and c are any numbers. This is the distributive property of multiplication over addition, allowing simplification of expressions.
(a + 1)(b + 1) = ab + (a + b) + 1
a and b are numbers. This formula shows how the product increases when both numbers are increased by 1. It is useful in algebraic expansions.
ab + a + b + 1 = (a + 1)(b + 1)
Expanded form of the increase of the product when both numbers are incremented by 1. It illustrates the application of the distributive property.
(a + m)(b + n) = ab + mb + an + mn
a, b, m, and n are integers. This identity depicts the product of two binomials, indicating how each term interacts.
a(b – v) = ab - av
This identity shows the effect of decreasing b by v in the multiplication of a and b, useful for simplifying expressions with subtractions.
(a + u)(b + v) = ab + ub + av + uv
This formula represents the multiplication of two binomials and shows how the structure of the expression influences its total value.
x(y + z) = xy + xz
x, y, and z are variables. Represents distributive property showing how multiplication distributes over addition.
(a + b)(a + b) = a² + 2ab + b²
This is a perfect square expansion formula, useful for recognizing patterns in multiplication of sums.
x(a + b + c) = xa + xb + xc
Demonstrates distributivity with three terms. Useful for expanding expressions systematically.
a(b – c) = ab - ac
This illustrates the effect of subtracting c from b while multiplying by a, demonstrating practical uses in algebra.
Equations
(x + 2)(y + 3) = xy + 3x + 2y + 6
This equation expands two binomials, illustrating how distributive property applies in algebra.
23(27 + 1) = 23 × 27 + 23
Example of how the product increases by a when one factor is incremented, showcasing a specific application of distributivity.
(a + 1)(b - 1) = ab + b - a - 1
Shows the relationship when one number is increased by 1 and the other is decreased by 1, expanding on the distributive property.
(a + u)(b - v) = ab + ub - av - uv
A generalized formula showing the expansion of an addition and subtraction involving two variables.
x(y + z) = xy + xz
Reiterates the distributive property, relevant for various algebraic applications.
(7)(y + 5) = 7y + 35
Illustration of distributive property in a numerical context, simplifying the expression effectively.
(a + b)(c + d) = ac + ad + bc + bd
This is a straightforward application of distributive property across two binomials, fundamental for algebraic expansions.
(4 + x)(3 - y) = 12 - 4y + 3x - xy
Shows complex interactions in expressions using the distributive property, demonstrating multiple real-world applications.
x(a + b + c) = xa + xb + xc
Expands a single variable multiplied by a trinomial, demonstrating the versatility of the distributive property.
(a + b)(a + b) = a² + 2ab + b²
Demonstrates the formula for a square binomial and its relevance in algebraic simplifications.
