Factorise (3p -q)² -4(3p - q) + 4 then its value is
(3p + q +2)²
(3p + q -2)²
(3p - q + 2)²
(3p - q -2)²
Answers
Answer:
9
2
−
6
+
2
−
1
2
+
4
+
4
Step-by-step explanation:
How to solve your problem
(
3
−
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2
−
4
(
3
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+
4
(3p-q)^{2}-4(3p-q)+4
(3p−q)2−4(3p−q)+4
Simplify
1
Expand the square
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3
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2
−
4
(
3
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+
4
\left(3p-q\right)^{2}-4(3p-q)+4
(3p−q)2−4(3p−q)+4
(
3
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(
3
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−
4
(
3
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+
4
(3p-q)(3p-q)-4(3p-q)+4
(3p−q)(3p−q)−4(3p−q)+4
2
Distribute
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3
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(
3
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−
4
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+
4
{\color{#c92786}{(3p-q)(3p-q)}}-4(3p-q)+4
(3p−q)(3p−q)−4(3p−q)+4
3
(
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+
(
3
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(
−
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−
4
(
3
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+
4
{\color{#c92786}{3p(3p-q)+(3p-q)\left(-q\right)}}-4(3p-q)+4
3p(3p−q)+(3p−q)(−q)−4(3p−q)+4
3
Distribute
3
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+
(
3
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(
−
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−
4
(
3
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+
4
{\color{#c92786}{3p(3p-q)}}+(3p-q)\left(-q\right)-4(3p-q)+4
3p(3p−q)+(3p−q)(−q)−4(3p−q)+4
9
2
−
3
+
(
3
−
)
(
−
)
−
4
(
3
−
)
+
4
{\color{#c92786}{9p^{2}-3pq}}+(3p-q)\left(-q\right)-4(3p-q)+4
9p2−3pq+(3p−q)(−q)−4(3p−q)+4
4
Re-order terms so that constants are on the left
9
2
−
3
+
(
3
−
)
(
−
)
−
4
(
3
−
)
+
4
9p^{2}-3pq+(3p-q)\left(-q\right)-4(3p-q)+4
9p2−3pq+(3p−q)(−q)−4(3p−q)+4
9
2
−
3
−
(
3
−
)
⋅
−
4
(
3
−
)
+
4
9p^{2}-3pq-(3p-q) \cdot q-4(3p-q)+4
9p2−3pq−(3p−q)⋅q−4(3p−q)+4
5
Distribute
9
2
−
3
−
(
3
−
)
⋅
−
4
(
3
−
)
+
4
9p^{2}-3pq-{\color{#c92786}{(3p-q) \cdot q}}-4(3p-q)+4
9p2−3pq−(3p−q)⋅q−4(3p−q)+4
9
2
−
3
−
(
3
+
(
−
)
)
−
4
(
3
−
)
+
4
9p^{2}-3pq-\left({\color{#c92786}{3pq+q\left(-q\right)}}\right)-4(3p-q)+4
9p2−3pq−(3pq+q(−q))−4(3p−q)+4
6
Re-order terms so that constants are on the left
9
2
−
3
−
(
3
+
(
−
)
)
−
4
(
3
−
)
+
4
9p^{2}-3pq-\left(3pq+q\left(-q\right)\right)-4(3p-q)+4
9p2−3pq−(3pq+q(−q))−4(3p−q)+4
9
2
−
3
−
(
3
−
)
−
4
(
3
−
)
+
4
9p^{2}-3pq-\left(3pq-qq\right)-4(3p-q)+4
9p2−3pq−(3pq−qq)−4(3p−q)+4
7
Combine exponents
9
2
−
3
−
(
3
−
)
−
4
(
3
−
)
+
4
9p^{2}-3pq-\left(3pq-{\color{#c92786}{qq}}\right)-4(3p-q)+4
9p2−3pq−(3pq−qq)−4(3p−q)+4
9
2
−
3
−
(
3
−
2
)
−
4
(
3
−
)
+
4
9p^{2}-3pq-\left(3pq-{\color{#c92786}{q^{2}}}\right)-4(3p-q)+4
9p2−3pq−(3pq−q2)−4(3p−q)+4
8
Distribute
9
2
−
3
−
(
3
−
2
)
−
4
(
3
−
)
+
4
9p^{2}-3pq-\left(3pq-q^{2}\right)-4(3p-q)+4
9p2−3pq−(3pq−q2)−4(3p−q)+4
9
2
−
3
−
3
+
2
−
4
(
3
−
)
+
4
9p^{2}-3pq-3pq+q^{2}-4(3p-q)+4
9p2−3pq−3pq+q2−4(3p−q)+4
9
Combine like terms
9
2
−
3
−
3
+
2
−
4
(
3
−
)
+
4
9p^{2}{\color{#c92786}{-3pq}}{\color{#c92786}{-3pq}}+q^{2}-4(3p-q)+4
9p2−3pq−3pq+q2−4(3p−q)+4
9
2
−
6
+
2
−
4
(
3
−
)
+
4
9p^{2}{\color{#c92786}{-6pq}}+q^{2}-4(3p-q)+4
9p2−6pq+q2−4(3p−q)+4
10
Distribute
9
2
−
6
+
2
−
4
(
3
−
)
+
4
9p^{2}-6pq+q^{2}{\color{#c92786}{-4(3p-q)}}+4
9p2−6pq+q2−4(3p−q)+4
9
2
−
6
+
2
−
1
2
+
4
+
4
Your answer is
(3p-q+2)
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