Write in Standard Form (x+2)^2(x-1)^2

${(x + 2)}^{2} {(x - 1)}^{2}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Rewrite ${(x + 2)}^{2}$ as $(x + 2) (x + 2)$ .

$(x + 2) (x + 2) {(x - 1)}^{2}$

Expand $(x + 2) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$(x (x + 2) + 2 (x + 2)) {(x - 1)}^{2}$

Apply the distributive property.

$(x \cdot x + x \cdot 2 + 2 (x + 2)) {(x - 1)}^{2}$

Apply the distributive property.

$(x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) {(x - 1)}^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$(x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) {(x - 1)}^{2}$

Move $2$ to the left of $x$ .

$(x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) {(x - 1)}^{2}$

Multiply $2$ by $2$ .

$(x^{2} + 2 x + 2 x + 4) {(x - 1)}^{2}$

Add $2 x$ and $2 x$ .

$(x^{2} + 4 x + 4) {(x - 1)}^{2}$

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$(x^{2} + 4 x + 4) ((x - 1) (x - 1))$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$(x^{2} + 4 x + 4) (x (x - 1) - 1 (x - 1))$

Apply the distributive property.

$(x^{2} + 4 x + 4) (x \cdot x + x \cdot - 1 - 1 (x - 1))$

Apply the distributive property.

$(x^{2} + 4 x + 4) (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$(x^{2} + 4 x + 4) (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Move $- 1$ to the left of $x$ .

$(x^{2} + 4 x + 4) (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1)$

Rewrite $- 1 x$ as $- x$ .

$(x^{2} + 4 x + 4) (x^{2} - x - 1 x - 1 \cdot - 1)$

Rewrite $- 1 x$ as $- x$ .

$(x^{2} + 4 x + 4) (x^{2} - x - x - 1 \cdot - 1)$

Multiply $- 1$ by $- 1$ .

$(x^{2} + 4 x + 4) (x^{2} - x - x + 1)$

Subtract $x$ from $- x$ .

$(x^{2} + 4 x + 4) (x^{2} - 2 x + 1)$

Expand $(x^{2} + 4 x + 4) (x^{2} - 2 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x^{2} + x^{2} (- 2 x) + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 2} + x^{2} (- 2 x) + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Add $2$ and $2$ .

$x^{4} + x^{2} (- 2 x) + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Rewrite using the commutative property of multiplication.

$x^{4} - 2 x^{2} x + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$x^{4} - 2 (x \cdot x^{2}) + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{4} - 2 (x^{1} x^{2}) + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} - 2 x^{1 + 2} + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Add $1$ and $2$ .

$x^{4} - 2 x^{3} + x^{2} \cdot 1 + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x^{2}$ by $1$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x \cdot x^{2} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{4} - 2 x^{3} + x^{2} + 4 (x^{2} x) + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{4} - 2 x^{3} + x^{2} + 4 (x^{2} x^{1}) + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} - 2 x^{3} + x^{2} + 4 x^{2 + 1} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Add $2$ and $1$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} + 4 x (- 2 x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Rewrite using the commutative property of multiplication.

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} + 4 \cdot - 2 x \cdot x + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} + 4 \cdot - 2 (x \cdot x) + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $x$ by $x$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} + 4 \cdot - 2 x^{2} + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $4$ by $- 2$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} - 8 x^{2} + 4 x \cdot 1 + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $4$ by $1$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} - 8 x^{2} + 4 x + 4 x^{2} + 4 (- 2 x) + 4 \cdot 1$

Multiply $- 2$ by $4$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} - 8 x^{2} + 4 x + 4 x^{2} - 8 x + 4 \cdot 1$

Multiply $4$ by $1$ .

$x^{4} - 2 x^{3} + x^{2} + 4 x^{3} - 8 x^{2} + 4 x + 4 x^{2} - 8 x + 4$

Simplify by adding terms.

Add $- 2 x^{3}$ and $4 x^{3}$ .

$x^{4} + 2 x^{3} + x^{2} - 8 x^{2} + 4 x + 4 x^{2} - 8 x + 4$

Subtract $8 x^{2}$ from $x^{2}$ .

$x^{4} + 2 x^{3} - 7 x^{2} + 4 x + 4 x^{2} - 8 x + 4$

Add $- 7 x^{2}$ and $4 x^{2}$ .

$x^{4} + 2 x^{3} - 3 x^{2} + 4 x - 8 x + 4$

Subtract $8 x$ from $4 x$ .

$x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4$

Write in Standard Form (x+2)^2(x-1)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.