Algebra 1- A complete guide to learning algebra

Explore the language of algebra by learning variables, algebraic expressions, and equations, and master operation vocabulary for addition, subtraction, multiplication, and division with examples.

Explore algebraic expressions by identifying like terms and coefficients, then combine like terms to simplify expressions and solve basic word problems.

Master how to multiply and divide algebraic expressions, combine like terms, and apply exponent rules to simplify polynomials and rational expressions with variables.

Expand algebraic expressions by distributing outside terms across brackets, handle positive and negative signs, and combine like terms with practical examples.

Explore binomial expansion by multiplying two binomials, such as 3y+2 and 4y-5, collecting like terms to yield the quadratic 12y^2-7y-10, with two methods yielding the same result.

Explore evaluating algebraic expressions by applying the order of operations with brackets, exponents, and substitution, solving examples that combine addition, subtraction, multiplication, and division.

Identify and extract the highest common factor to factorize algebraic expressions, recognizing factorization as the reverse of expansion. Verify results by expanding the factors to recover the original expression.

Learn how to solve simple linear equations using the balance method or moving terms across the equality, check solutions, and understand expressions like X+6=11 and 12=2X-8, with X=5 or X=10.

Learn to solve linear equations with the variable on both sides by grouping like terms, moving constants, and dividing to isolate x, with example checks.

Expand the brackets and collect like terms to solve for x in linear equations involving brackets; verify the solution by checking both sides.

Solve equations with brackets and the unknown on both sides by expanding brackets, collecting like terms, and checking the solution on both sides.

Solve linear equations from word problems by modeling area with length times breadth to find X, then verify the result.

Eliminate one unknown in a pair of simultaneous equations using the elimination method, balance coefficients, solve for x, then substitute to find y, and verify.

Solve simultaneous linear equations using the substitution method by rearranging one equation to express a variable, substituting into the other, solving for x, then y, and checking both equations.

Learn to solve problem with simultaneous equations by setting x - y = 7 and x + y = 25 using elimination, yielding x = 16 and y = 9.

Change the subject of a formula by rewriting it in terms of the desired unknown, remove denominator by multiplying through, and isolating the variable with division, multiplication, and square roots.

Explore factorization by grouping of quadratic expressions, showing how Y^2+5Y-3Y-15 factors to (Y+5)(Y-3) and 4B^2-6AB+18BC-27C to (2B-3A)(2B+9C) as the reverse of expansion.

Factorize with the difference of two squares by taking square roots of squared terms, yielding (a-b)(a+b); for example, x^2-16=(x-4)(x+4) and 9x^2-16y^2=(3x-4y)(3x+4y).

Learn to factor quadratic expressions by identifying factor pairs that multiply to ac and sum to b, split the middle term, and factor by grouping to obtain (x+3)(x+4) and (7x+3)(x-2).

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and learn how factorization works when the leading coefficient differs from one, to find roots.

Learn to simplify algebraic fractions by factoring and canceling common factors, using examples of factoring out x and quadratic expressions to produce simplified results.

Explains multiplying and dividing algebraic fractions, applying reciprocal for division, and simplifying with no common factors using examples.

learn to add and subtract algebraic fractions by applying common denominators, expanding and combining like terms to simplify the final result.

Find a system with a linear and a quadratic by substituting y=3-x. Find the quadratic x^2-3x+2=0, which factors to (x-1)(x-2)=0, giving x=1 or x=2 and y values 2 and 1.

Solve the inequality -2x - 2 >= -5x + 1 by expanding brackets and collecting terms, yielding 3x >= -9 and x = -3.

Solve a linear inequality by applying a positive-integer domain constraint, showing the solution set is one to four on the number line.

Explore solving a word problem with inequalities: translate 'five plus four times a number' into 4x+5 ≤ 2x+19, apply negative division rule to get x ≤ 7.