Expanded form algebra
Introduction to Expanded form algebra:
To expand a polynomial, simply multiply every term in one factor by each term in the other factor. the reverse process is called factorization. Expansion is normally easier to perform than factorization.
For example, to expand the polynomial: (y+1)(y+2), the y in (y+1) gets multiplied with the y and the 2 in (y+2). After this, the terms (products) are added together. Then the 1 gets multiplied with the y and 2 in (y+2). Finally we get x2 + 3x + 2.
Example problems of Expanded form algebra:
Expanded form algebra problem 1:
Convert expanded form: x (x+5) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, x(x+5) = x*x +x*5
= x2+5x
Answer: x2+ 5x
Expanded form algebra problem 2:
Convert expanded form: (x-2) (x+7) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, (x-2) (x+7) = (x*x)-2(x) +(x*7)-2(7)
= x2-2x+7x-14
=x2+5x-14
Answer: x2+5x -14
Expanded form algebra problem 3:
Convert expanded form: 4x (5x+3) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, 4x (5x+3) = (4x*5x) + (4x*3)
= 20x2+ 12x
Answer: 20x2+12x
Expanded form algebra problem 4:
Convert expanded form: 4x+5 (8x) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, 4x+5 (8x) = (4x*8x) + (5*8x)
= 32x2+ 40x
Answer: 32x2+ 40x
Practice problems of Expanded form algebra:
To expand a polynomial, simply multiply every term in one factor by each term in the other factor. the reverse process is called factorization. Expansion is normally easier to perform than factorization.
For example, to expand the polynomial: (y+1)(y+2), the y in (y+1) gets multiplied with the y and the 2 in (y+2). After this, the terms (products) are added together. Then the 1 gets multiplied with the y and 2 in (y+2). Finally we get x2 + 3x + 2.
Example problems of Expanded form algebra:
Expanded form algebra problem 1:
Convert expanded form: x (x+5) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, x(x+5) = x*x +x*5
= x2+5x
Answer: x2+ 5x
Expanded form algebra problem 2:
Convert expanded form: (x-2) (x+7) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, (x-2) (x+7) = (x*x)-2(x) +(x*7)-2(7)
= x2-2x+7x-14
=x2+5x-14
Answer: x2+5x -14
Expanded form algebra problem 3:
Convert expanded form: 4x (5x+3) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, 4x (5x+3) = (4x*5x) + (4x*3)
= 20x2+ 12x
Answer: 20x2+12x
Expanded form algebra problem 4:
Convert expanded form: 4x+5 (8x) =?
Solution:
We can convert factored form to expanded form. So here multiply every term in one factor by each term in the other factor.
Therefore, 4x+5 (8x) = (4x*8x) + (5*8x)
= 32x2+ 40x
Answer: 32x2+ 40x
Practice problems of Expanded form algebra:
- Convert expanded form: 3x + (9-2x) =?
- Convert expanded form: (2x -3) (x+5) =?
- Convert expanded form: x (x+9) =?
- 27x-6x2
- 2x2+7x-15
- x2+9x