The problem asks to factor the expression $9x^2 - 49$ using the difference of squares factorization.

AlgebraDifference of SquaresFactorizationAlgebraic Expressions
2025/3/25

1. Problem Description

The problem asks to factor the expression 9x2499x^2 - 49 using the difference of squares factorization.

2. Solution Steps

The expression 9x2499x^2 - 49 is a difference of two squares. We can rewrite it as (3x)2(7)2(3x)^2 - (7)^2. The difference of squares factorization is given by:
a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)
In this case, a=3xa = 3x and b=7b = 7. Substituting these values into the formula, we get:
(3x)2(7)2=(3x7)(3x+7)(3x)^2 - (7)^2 = (3x - 7)(3x + 7)

3. Final Answer

(3x7)(3x+7)(3x - 7)(3x + 7)

Related problems in "Algebra"

The problem has three parts: (a) Factorize completely $2\pi h + 2\pi r^2$. (b) Express $\frac{4}{x+5...

FactorizationRational ExpressionsSimultaneous EquationsLinear Equations
2025/6/11

The problem is to solve the following five linear equations: 1. $8 - 8x = 9 - 9x$

Linear EquationsSolving Equations
2025/6/10

The problem is about the quadratic function $y = -2x^2 + (a+3)x + a - 3$. (1) Find the condition on ...

Quadratic FunctionsDiscriminantVieta's FormulasVertex of ParabolaIsosceles Right Triangle
2025/6/10

The problem consists of several sub-problems covering various topics in algebra. These include expre...

Scientific NotationEngineering NotationSimplificationPolynomial Remainder TheoremSimultaneous EquationsLogarithmic EquationsLinear EquationsGradientY-interceptEquation of a LinePartial Fractions
2025/6/10

We are given four problems: a) i. Use the vertical line test to show that $f(x) = \sqrt{x}$ is a fun...

FunctionsVertical Line TestRangeLinear FunctionsInverse FunctionsAlgebraic Manipulation
2025/6/10

We are given the equation $x^3 + 2x^2y - x^2 + 2xy + 4y^2 - 2y = 44$. The problem asks us to factor...

Polynomial FactorizationEquation SolvingInteger Properties
2025/6/10

We are given the equation $f(x) - g(x) = 3ax^2 + 2(a+1)x + a + 1$. We are also given that $a = \fra...

Quadratic EquationsParabolasIntersection of CurvesSystems of Equations
2025/6/10

Given that $f(x) - g(x) = 3ax^2 + 2(a+1)x + a+1$, we need to find the range of values for $a$ such t...

Quadratic InequalitiesQuadratic EquationsDiscriminantParabolasIntersection Points
2025/6/10

The problem is a fill-in-the-blank question. Given that for all real numbers $x$, $f(x) > g(x)$, det...

InequalitiesQuadratic FunctionsIntersection of CurvesProblem Solving
2025/6/10

The problem gives two quadratic functions $f(x) = 2ax^2 + (2a+1)x + a$ and $g(x) = -ax^2 - x - 1$. (...

Quadratic EquationsDiscriminantInequalitiesParabolas
2025/6/10