Solve (x+1)(x+3)-x=x²: Expanding Brackets and Simplifying

Q: Why does the x² cancel out on both sides?

After expanding and simplifying, you get $ x^2 + 3x + 3 = x^2 $. Since x² appears on both sides, subtracting x² from both sides eliminates it, leaving you with a linear equation!

Q: What if I expand the brackets wrong?

Use FOIL to be systematic: First × First, Outer × Outer, Inner × Inner, Last × Last. For (x+1)(x+3): x×x + x×3 + 1×x + 1×3 = x² + 3x + x + 3.

Q: How do I know when to move terms to the other side?

Move terms to collect like terms together. Since you have x² on both sides, subtract x² from both sides. Then collect all x terms and constants separately.

Linear Equations with Expanding Brackets

$(x+1)(x+3)-x=x^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Open parentheses properly, multiply each factor by each factor

00:22 Calculate the multiplications

00:25 Group factors

00:29 Simplify what's possible

00:38 Isolate X

00:47 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$(x+1)(x+3)-x=x^2$

Step-by-step solution

Let's solve the equation, first we'll simplify the algebraic expressions using the extended distribution law:

$(a+b)(c+d)=ac+ad+bc+bd$ We will therefore apply the mentioned law and open the parentheses in the expression in the equation:

$(x+1)(x+3)-x=x^2 \\ x^2+3x+x+3 -x=x^2 \\$ We'll continue and combine like terms, by moving terms, then - we can notice that the squared term cancels out and therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$x^2+3x+x+3 -x=x^2\\ 3x=-3\hspace{8pt}\text{/}:3\\ \boxed{x=-1}$ Therefore, the correct answer is answer A.

Final Answer

$x=-1$

Key Points to Remember

Essential concepts to master this topic

Distribution: Apply (a+b)(c+d) = ac + ad + bc + bd
Technique: Combine like terms: $3x + x - x = 3x$
Check: Substitute x = -1: $(-1+1)(-1+3) - (-1) = 1 = (-1)^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute all terms when expanding brackets
Don't expand (x+1)(x+3) as just x² + 3x = wrong result! This misses the cross terms and constant. Always multiply each term in the first bracket by each term in the second bracket using FOIL or the distributive property.

Practice Quiz

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$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why does the x² cancel out on both sides?

After expanding and simplifying, you get $x^2 + 3x + 3 = x^2$ . Since x² appears on both sides, subtracting x² from both sides eliminates it, leaving you with a linear equation!

What if I expand the brackets wrong?

Use FOIL to be systematic: First × First, Outer × Outer, Inner × Inner, Last × Last. For (x+1)(x+3): x×x + x×3 + 1×x + 1×3 = x² + 3x + x + 3.

How do I know when to move terms to the other side?

Move terms to collect like terms together. Since you have x² on both sides, subtract x² from both sides. Then collect all x terms and constants separately.

Why is x = -1 the only answer when it started as x²?

Even though the original equation looks quadratic, after expanding and simplifying, the x² terms cancel out! This creates a linear equation (3x = -3) with only one solution.

Can I check my answer a different way?

Yes! Substitute x = -1 into each part:

(x+1)(x+3) becomes (0)(2) = 0
Subtract x: 0 - (-1) = 1
Right side: (-1)² = 1

Both sides equal 1, so it's correct!

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